{"id":4345,"date":"2020-03-21T18:02:33","date_gmt":"2020-03-21T09:02:33","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?p=4345"},"modified":"2020-03-26T16:32:58","modified_gmt":"2020-03-26T07:32:58","slug":"sasa-textbook-math1-02","status":"publish","type":"post","link":"https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-02\/","title":{"rendered":"[\uc218\ud559\u2160] \uc81c1\uc7a5 \uc9d1\ud569\uacfc \ub17c\ub9ac\uc758 \uae30\ucd08(2)"},"content":{"rendered":"<style type=\"text\/css\">\nspan.hfill {\nfloat: right; \n}\n<\/style>\n<p><!-- \n\n\n<h2 style=\"text-align: center; margin-top: 1em; margin-bottom: 0.5em;\"> \uc81c1\uc7a5 \uc7a5\uc81c\ubaa9 <\/h2>\n\n\n\n\n<h2> 1.1 \uc808\uc81c\ubaa9 <\/h2>\n\n\n\n\n<h3> \uc18c\uc808\uc81c\ubaa9 <\/h3>\n\n\n <span class=\"defined\"> \ubcfc\ub4dc<\/span>\n\n\n\n<p> <span class=\"definition\"> \ubcf4\uae30 <\/span>\n\ubcf4\uae30 \ub0b4\uc6a9\n\n\n<ol class=\"parenthesis\"> \n\t\n\n<li> \uad04\ud638 \ubc88\ud638 \ubaa9\ub85d <\/li>\n\n\n<\/ol>\n\n\n<\/p>\n\n\n\n<img decoding=\"async\" src=\"https:\/\/coslimites.com\/wp-content\/uploads\/2020\/03\/fig-101.png\" alt=\"\" width=\"150\" height=\"150\" class=\"aligncenter size-full wp-image-1936\" \/>\n[efn_note]\ud517\ub178\ud2b8[\/efn_note]\n\n\n\n<div class=\"definition\">\n\t\n\n<p>\n\t\t<span class=\"definition\"> Definition 1.1.1 <\/span>\n\uc815\uc758 \ub0b4\uc6a9\n<\/p>\n\n<\/div>\n\n\n\n\n\n<blockquote>\n\uc778\uc6a9\ubb38\n<\/blockquote>\n\n\n\n\n\n<p>\n\t\t<span class=\"definition\"> \uc608\uc81c 1.1<\/span>\n\uc608\uc81c \ub0b4\uc6a9 \ud639\uc740 \uc720\uc81c\n<\/p>\n\n\n\n\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Sol.<\/span>\n\ud480\uc774 \ub610\ub294 \uc99d\uba85\n<span class=\"qed\"><\/span>\n<\/p>\n\n\n\n\n\n\n<div class=\"theorem\">\n\t\n\n<p>\n\t\t<span class=\"theorem\"> Theorem 1.1.3 <\/span>\n\uc815\ub9ac \ub0b4\uc6a9\n<\/p>\n\n\n<\/div>\n\n\n--><\/p>\n<h3> \uc5f0\uc5ed\uc801 \ucd94\ub860<\/h3>\n<p>\n\ub450 \uc870\uac74 \\(p, q\\)\uc5d0 \ub300\ud558\uc5ec, \ubb38\uc7a5 &#8216;\\(p\\longrightarrow q\\)&#8217;\ub294 \ud558\ub098\uc758 \uba85\uc81c\uac00 \ub41c\ub2e4. \uc77c\ubc18\uc801\uc73c\ub85c \uc870\uac74 \\(p, q\\)\uc758 \uc9c4\ub9ac\uc9d1\ud569\uc744 \uac01\uac01 \\(P, Q\\)\ub77c \ud560 \ub54c,  \\(p\\longrightarrow q\\)\uac00 \ucc38\uc774\uba74 \uc870\uac74 \\(p\\)\ub97c \ucc38\uc774\ub418\uac8c \ud558\ub294 \uc6d0\uc18c\ub294 \uc870\uac74 \\(q\\)\ub3c4 \ucc38\uc774 \ub418\uac8c \ud558\ubbc0\ub85c \\(P\\subset Q\\)\uc778 \uad00\uacc4\uac00 \uc131\ub9bd\ud55c\ub2e4. \ub610\ud55c \\(P\\subset Q\\)\uc778 \uad00\uacc4\uac00 \uc788\uc73c\uba74 \uba85\uc81c \\(p\\longrightarrow q\\)\ub294 \ucc38\uc774\ub2e4. \ud55c\ud3b8, \uba85\uc81c \\(p\\longrightarrow q\\)\uac00 \uac70\uc9d3\uc774\ub77c\ub294 \uac83\uc740 \uc870\uac74 \\(p\\)\uac00 \ucc38\uc774 \ub418\uc9c0\ub9cc \\(q\\)\ub294 \ucc38\uc774 \ub418\uc9c0 \uc54a\ub294 \uc6d0\uc18c\uac00 \uc788\uc74c\uc744 \ub9d0\ud558\uba70 \uc774\ub294 \uace7 \\(P\\not\\subset Q\\)\uc784\uc744 \ub73b\ud55c\ub2e4. \uc774\uc0c1\uc744 \uc815\ub9ac\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.\n<\/p>\n<div class=\"theorem\">\n<p>\n\t\t<span class=\"theorem\"> Theorem 1.1.4 <\/span> (\uba85\uc81c \\(p\\longrightarrow q\\)\uc758 \ucc38\uacfc \uac70\uc9d3) <br \/>\n\uc870\uac74 \\(p, q\\)\uc758 \uc9c4\ub9ac\uc9d1\ud569 \\(P, Q\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ol class=\"parenthesis-roman\">\n<li> \\(P\\subset Q\\)\uc77c \ub54c, \uba85\uc81c \\(p\\longrightarrow q\\)\ub294 \ucc38\uc774\ub2e4. <\/li>\n<li> \\(P\\not\\subset Q\\)\uc77c \ub54c, \uba85\uc81c \\(p\\longrightarrow q\\)\ub294 \uac70\uc9d3\uc774\ub2e4. <\/li>\n<\/ol>\n<\/div>\n<p>\n\uba85\uc81c \\(p\\longrightarrow q\\)\uac00 \uac70\uc9d3\uc784\uc744 \ubcf4\uc774\uae30 \uc704\ud574\uc11c\ub294 \\(p\\)\ub97c \ub9cc\uc871\uc2dc\ud0a4\uc9c0\ub9cc,  \\(q\\)\ub97c \ub9cc\uc871\uc2dc\ud0a4\uc9c0 \uc54a\ub294 \uc608\ub97c \ud558\ub098\ub77c\ub3c4 \ubcf4\uc774\uba74 \ub41c\ub2e4. \uc989 \\(x\\in P\\)\uc774\uace0 \\(x\\not\\in Q\\)\uc778 \\(x\\)\uac00 \uc788\uc74c\uc744 \ubcf4\uc774\uba74 \ub41c\ub2e4. \uc774\uac19\uc740 \uc608\ub97c <span class=\"defined\">\ubc18\ub840<\/span>(counter example)\ub77c\uace0 \ud55c\ub2e4. \uc608\ub97c \ub4e4\uc5b4  \uba85\uc81c<br \/>\n\\[<br \/>\n\\mbox{\\(x\\)\uac00 \\(4\\)\uc758 \uc57d\uc218\uc774\uba74 \\(x\\)\ub294 \\(6\\)\uc758 \uc57d\uc218\uc774\ub2e4.}<br \/>\n\\]<br \/>\n\uc758 \ubc18\ub840\ub85c \\(4\\)\ub97c \uc7a1\uc744 \uc218 \uc788\ub2e4.\n<\/p>\n<div class=\"definition\">\n<p>\n\t\t<span class=\"definition\"> Remark <\/span><br \/>\n\uc804\uccb4\uc9d1\ud569\uc774 \ubb34\uc5c7\uc774\ub0d0\uc5d0 \ub530\ub77c \uba85\uc81c \\(p\\longrightarrow q\\)\uc758 \ucc38, \uac70\uc9d3\uc740 \ub2ec\ub77c\uc9c8 \uc218 \uc788\ub2e4. \ubcf4\ud1b5\uc758 \uace0\ub4f1\ud559\uad50 \uacfc\uc815\uc5d0\uc11c\ub294 (\uc218\ub97c \ub2e4\ub8e8\ub294 \uc870\uac74\uc5d0\uc11c) \ubcc4\ub2e4\ub978 \uc5b8\uae09\uc774 \uc5c6\uc744 \ub54c\ub294 \uc804\uccb4\uc9d1\ud569\uc744 \uc2e4\uc218 \uc804\uccb4\uc758 \uc9d1\ud569\uc774\ub77c\uace0 \uc0dd\uac01\ud55c\ub2e4.\n<\/p>\n<\/div>\n<p>\n\ud569\uc131\uba85\uc81c \uc911\uc5d0\ub294 \\(\\sim p\\vee p\\)\uc640 \uac19\uc774 \uadf8 \uc9c4\ub9bf\uac12\uc774 \ud56d\uc0c1 \ucc38\uc778 \uac83\uc774 \uc788\ub2e4. \uadf8\ub9ac\uace0 \\(\\sim p\\wedge p\\)\uc640 \uac19\uc774 \uadf8 \uc9c4\ub9bf\uac12\uc774 \ud56d\uc0c1 \uac70\uc9d3\uc778 \uac83\ub3c4 \uc788\ub2e4. \uc774\ub807\uac8c \ubaa8\ub4e0 \ub17c\ub9ac\uc801 \uac00\ub2a5\uc131\uc758 \uac01 \uacbd\uc6b0\ub9c8\ub2e4 \uc9c4\ub9bf\uac12\uc774 \ucc38\uc778 \uba85\uc81c\ub97c <span class=\"defined\">\ud56d\uc9c4\uba85\uc81c<\/span>(tautology)\ub77c\uace0 \ud55c\ub2e4. \uadf8\ub9ac\uace0 \ubaa8\ub4e0 \ub17c\ub9ac\uc801 \uac00\ub2a5\uc131\uc758 \uac01 \uacbd\uc6b0\ub9c8\ub2e4 \uc9c4\ub9bf\uac12\uc774 \uac70\uc9d3\uc778 \uba85\uc81c\ub97c <span class=\"defined\">\ubaa8\uc21c\uba85\uc81c<\/span>(contradiction)\ub77c\uace0 \ud55c\ub2e4. \ud56d\uc9c4\uba85\uc81c\ub294 \ubcf4\ud1b5 \\(t\\)\ub85c \ud45c\uae30\ud558\uace0 \ubaa8\uc21c\uba85\uc81c\ub294 \ubcf4\ud1b5 \\(c\\)\ub85c \ud45c\uae30\ud55c\ub2e4.\n<\/p>\n<p>\n\ub450 \uba85\uc81c \ud639\uc740 \uc870\uac74 \\(p, q\\)\uc5d0 \ub300\ud558\uc5ec \uba85\uc81c \\(p\\longrightarrow q\\)\uac00 \ucc38\uc77c \ub54c, \uc774\ub97c<br \/>\n\\[<br \/>\np\\Longrightarrow q<br \/>\n\\]<br \/>\n\uc640 \uac19\uc774 \ub098\ud0c0\ub0b4\uba70 &#8216;\\(p\\)\ub294 \\(q\\)\ub97c \ud568\uc758\ud55c\ub2e4.&#8217;\ub77c\uace0 \uc77d\ub294\ub2e4. \uc774 \ub54c \\(p\\)\ub294 \\(q\\)\uc774\uae30 \uc704\ud55c <span class=\"defined\">\ucda9\ubd84\uc870\uac74<\/span>\uc774\ub77c\uace0 \ud558\uba70 \\(q\\)\ub294 \\(p\\)\uc774\uae30 \uc704\ud55c <span class=\"defined\">\ud544\uc694\uc870\uac74<\/span>\uc774\ub77c\uace0 \ud55c\ub2e4. \ub610\ud55c \uc30d\uc870\uac74\ubb38 \\(p\\longleftrightarrow q\\)\uac00 \ucc38\uc77c \ub54c \uc774\uac83\uc744 \\(p\\Longleftrightarrow q\\)\ub85c \ub098\ud0c0\ub0b4\uace0, &#8216;\\(p\\)\uc640 \\(q\\)\ub294 \ub3d9\uce58\uc774\ub2e4.\u2019\ub77c\uace0 \ud55c\ub2e4. \uc774\ub54c \\(p\\)\ub294 \\(q\\)\uc758 <span class=\"defined\">\ud544\uc694\ucda9\ubd84\uc870\uac74<\/span>\uc774\uba70 \\(q\\)\ub294 \\(p\\)\uc758 \ud544\uc694\ucda9\ubd84\uc870\uac74\uc774\ub2e4. \ubcf4\ud1b5 \uc30d\uc870\uac74\ubb38 \\(p\\Longleftrightarrow q\\)\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uc77d\uace4 \ud55c\ub2e4.<\/p>\n<ul>\n<li> \\(p\\)\uc640 \\(q\\)\ub294 \uc11c\ub85c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc774\ub2e4. <\/li>\n<li> \\(p\\)\uc774\uba74 \\(q\\)\uc774\uace0 \\(q\\)\uc774\uba74 \\(p\\)\uc774\ub2e4. <\/li>\n<li> \\(p\\)\uc774\uba74 \uadf8\ub9ac\uace0 \uadf8\ub54c\uc5d0\ub9cc \\(q\\)\uc774\ub2e4. <\/li>\n<\/ul>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 1.10 <\/span><br \/>\n \\([(p\\longrightarrow q)\\wedge (q\\longrightarrow r)]\\Longrightarrow [p\\longrightarrow r]\\)\uc784\uc744 \uc9c4\ub9ac\ud45c\ub97c \uc774\uc6a9\ud558\uc5ec \ud655\uc778\ud574 \ubcf4\uc544\ub77c.\n<\/p>\n<p>\n\uae30\ud638 \\(\\Longleftrightarrow\\)\uc640 \\(\\equiv\\)\ub294 \ub450 \uba85\uc81c\uac00 \ub3d9\uce58\ub77c\ub294 \uac83\uc744 \ub098\ud0c0\ub0bc \ub54c\uc5d0\ub3c4 \uc0ac\uc6a9\ub418\uae30\ub3c4 \ud558\uc9c0\ub9cc \uc5b4\ub5a0\ud55c \uac1c\ub150\uc744 \uc815\uc758\ud560 \ub54c\uc5d0\ub3c4 \uc0ac\uc6a9\ub41c\ub2e4. \uc774\ub97c\ud14c\uba74 \ubd80\ub4f1\ud638 \\(\\leq\\)\ub97c \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud560 \uc218 \uc788\ub2e4.<span id='easy-footnote-1-4345' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-02\/#easy-footnote-bottom-1-4345' title=' \uae30\ud638 \\(\\equiv\\)\ub294 \ubb38\uc790\ub098 \uac1c\ub150\uc744 \uc815\uc758\ud560 \ub54c\uc5d0 \uae30\ud638 \\(=\\)\uc744 \ub300\uc2e0\ud558\uc5ec \uc0ac\uc6a9\ub418\uae30\ub3c4 \ud55c\ub2e4. \uc608\ub97c \ub4e4\uc5b4 &amp;#8216;\\(f(x)\\equiv x^{2}+3\\)\uc77c \ub54c \\(f(1)=4\\)\uc774\ub2e4.&amp;#8217;\uc640 \uac19\uc774 \uc4f4 \uac83\uc740 \ud568\uc218 \\(f\\)\ub97c \\(x^{2}+3\\)\uc73c\ub85c \uc815\uc758\ud558\uba74 \\(f(1)\\)\uc740 \\(4\\)\uc640 \uac19\ub2e4.\u2019\ub77c\ub294 \ub73b\uc774\ub2e4. \ucc38\uace0\ub85c \uae30\ud638 \\(:=\\) \uc5ed\uc2dc \ubb38\uc790\ub098 \uae30\ud638\uc758 \ub73b\uc744 \uc815\uc758\ud560 \ub54c \ub9ce\uc774 \uc4f0\ub294 \uae30\ud638\uc774\ub2e4. \uc608\ub97c \ub4e4\uc5b4 \\(h:=a+3\\)\uc73c\ub85c \uc4f0\uba74 \\(h\\)\ub97c \\(a+3\\)\uc73c\ub85c \uc815\uc758\ud55c\ub2e4\ub294 \ub73b\uc774\ub2e4.'><sup>1<\/sup><\/a><\/span><br \/>\n\\[<br \/>\na\\leq b\\quad \\Longleftrightarrow\\quad (a< b \\vee a=b)\n\\]\n\uc774\uac83\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \ub098\ud0c0\ub0bc \uc218\ub3c4 \uc788\ub2e4.\n\\[\na\\leq b \\quad \\equiv\\quad (a< b \\vee a=b)\n\\]\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \ubcf4\uae30  <\/span><br \/>\n\ub17c\ub9ac\ud569, \ub17c\ub9ac\uacf1, \uc30d\uc870\uac74\uc758 \uc9c4\ub9ac\ud45c\ub97c \uc791\uc131\ud574\ubcf4\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<br \/>\n<img decoding=\"async\" src=\"https:\/\/coslimites.com\/wp-content\/uploads\/2020\/03\/tab-106.png\" alt=\"\" width=\"500\" height=\"\" class=\"aligncenter size-full wp-image-1936\" \/><br \/>\n\uc774 \uc9c4\ub9ac\ud45c\uc5d0 \uc758\ud574<br \/>\n\\begin{align*}<br \/>\np\\vee q\\quad &#038; \\Longleftrightarrow\\quad q\\vee p, \\\\<br \/>\np\\wedge q\\quad &#038; \\Longleftrightarrow\\quad q\\wedge p, \\\\<br \/>\np\\longleftrightarrow q\\quad &#038; \\Longleftrightarrow\\quad q\\longleftrightarrow p<br \/>\n\\end{align*}<br \/>\n\uc784\uc744 \uc54c \uc218 \uc788\ub2e4. \uc989 \uc704\uc758 \ud45c\ub85c\ubd80\ud130 \ub17c\ub9ac\ud569, \ub17c\ub9ac\uacf1, \uc30d\uc870\uac74\ubd80\ub294 \uad50\ud658\ubc95\uce59\uc774 \uc131\ub9bd\ud568\uc744 \ud655\uc778\ud560 \uc218 \uc788\ub2e4.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 1.11  <\/span><br \/>\n\uc9c4\ub9ac\ud45c\ub97c \uc774\uc6a9\ud558\uc5ec \ub17c\ub9ac\ud569\uacfc \ub17c\ub9ac\uacf1\uc758 \ubd84\ubc30\ubc95\uce59\uc774 \uc131\ub9bd\ud568\uc744 \ubcf4\uc5ec\ub77c. \uc989\\begin{align*}<br \/>\np\\wedge (q\\vee r)\\quad &#038; \\Longleftrightarrow\\quad (p\\wedge q)\\vee (p\\wedge r), \\\\<br \/>\np\\vee (q\\wedge r)\\quad &#038; \\Longleftrightarrow\\quad (p\\vee q) \\wedge (p\\vee r)<br \/>\n\\end{align*}<br \/>\n\uc774 \uc131\ub9bd\ud568\uc744 \ubcf4\uc5ec\ub77c.\n<\/p>\n<p>\n\uc218\ud559\uc774\ub098 \ub17c\ub9ac\uc5d0\uc11c\uc758 <span class=\"defined\">\uc815\ub9ac<\/span>(theorem)\ub780 \ucc38\uc778 \uba85\uc81c\ub4e4 \uc911 \uc911\uc694\ud55c \uc0ac\uc2e4\uc744 \uc77c\uceeb\ub294 \ub9d0\uc774\ub2e4. \uc774\ub7ec\ud55c \ucc38\uc778 \uba85\uc81c\uc778 \uc815\ub9ac\uc758 \uc815\ub2f9\uc131\uc744 \ubc1d\ud788\ub294 \uc77c\uc744 <span class=\"defined\">\uc99d\uba85<\/span>(proof)\uc774\ub77c\uace0 \ud55c\ub2e4. \ubcf4\ud1b5 \uba85\uc81c\ub294 &#8216;\\(\\cdots\\) \uc77c \ub54c \\(\\cdots\\)\uac00 \uc131\ub9bd\ud55c\ub2e4.&#8217;\uc640 \uac19\uc774 \uc870\uac74(\uac00\uc815)\uacfc \uacb0\ub860\uc73c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uc218\ud559\uc5d0\uc11c \ub2e4\ub8e8\ub294 \ubaa8\ub4e0 \uc815\ub9ac\uac00 \\(p\\Longrightarrow q\\)\uc758 \uaf34\uc774\ub77c\uace0 \ud574\ub3c4 \uacfc\uc5b8\uc774 \uc544\ub2c8\ub2e4. \uac00\uc815\uc73c\ub85c\ubd80\ud130 \uacb0\ub860\uae4c\uc9c0 \ub3c4\ub2ec\ud558\ub294 \uacfc\uc815\uc744 \ub17c\ub9ac\uc801\uc73c\ub85c \uc124\uba85\ud560 \ub54c\uc5d0\ub294 \uc815\uc758, \uadf8\ub9ac\uace0 \uae30\uc874\uc5d0 \uc99d\uba85\ud588\ub358 \uc815\ub9ac\ub9cc\uc744 \uc0ac\uc6a9\ud574\uc57c \ud55c\ub2e4. \ub2e4\uc74c \uc0c1\ud669\uc744 \uc0dd\uac01\ud574\ubcf4\uc790.\n<\/p>\n<blockquote><p>\n\uc544\ub984\uc774\ub294 \uc790\uc728\ud559\uc2b5\uc2dc\uac04\uc5d0 \uc218\ud559 \uacfc\uc81c\ub85c<br \/>\n\\[<br \/>\n(p\\longrightarrow q)\\quad \\Longleftrightarrow\\quad (\\sim q\\longrightarrow \\sim p)<br \/>\n\\]<br \/>\n\ub97c \uc99d\uba85\ud558\ub824\ub2e4\uac00 \uc606\uc790\ub9ac\uc5d0 \uc549\uc740 \uace0\uc6b4\uc774\ub3c4 \ub611\uac19\uc740 \uc219\uc81c\ub97c \ud558\uace0 \uc788\uc74c\uc744 \ubc1c\uacac\ud558\uc600\ub2e4. \uc544\ub984\uc774\ub294 \uc9c4\ub9ac\ud45c\ub97c \uadf8\ub9ac\uae30\uac00 \uadc0\ucc2e\uc544\uc11c \uace0\uc6b4\uc774\uc5d0\uac8c \uc9c4\ub9ac\ud45c\ub97c \ubcf4\uc5ec \ub2ec\ub77c\uace0 \ud558\uc600\ub2e4. \uadf8\ub7ac\ub354\ub2c8 \uace0\uc6b4\uc774\ub294 \uc9c4\ub9ac\ud45c\ub97c \uadf8\ub9ac\uc9c0 \uc54a\uace0 \uc99d\uba85\ud588\ub2e4\uba74\uc11c \uc544\ub984\uc774\uc5d0\uac8c \ub2e4\uc74c\uacfc \uac19\uc740 \uc2dd\uc744 \ubcf4\uc5ec\uc8fc\uc5c8\ub2e4.<br \/>\n\\begin{align*}<br \/>\n(p\\longrightarrow q)\\quad \\Longleftrightarrow\\quad (\\sim p\\ \\vee q)\\quad &#038; \\Longleftrightarrow\\quad (q\\ \\vee\\sim p) \\\\<br \/>\n &#038; \\Longleftrightarrow\\quad [\\sim(\\sim q)\\vee (\\sim p)]  \\\\<br \/>\n&#038; \\Longleftrightarrow\\quad \\sim q\\longrightarrow \\sim p<br \/>\n\\end{align*}\n<\/p><\/blockquote>\n<ul>\n<li> \uace0\uc6b4\uc774\uac00 \ubcf4\uc5ec\uc900 \uc2dd\uc744 \uc99d\uba85\uc73c\ub85c\uc11c \uc778\uc815\ud560 \uc218 \uc788\ub294\uac00?<\/li>\n<li> \uc9c4\ub9ac\ud45c\ub97c \uc791\uc131\ud558\ub294 \uac83\uacfc \uc704\uc640 \uac19\uc740 \ubc29\ubc95 \uc911 \uc5b4\ub290 \uac83\uc774 \ub354 \uac04\ub2e8\ud558\uaca0\ub294\uac00?<\/li>\n<\/ul>\n<p>\n\uc9c4\ub9ac\ud45c\ub97c \uc0ac\uc6a9\ud558\uc9c0 \uc54a\uace0 \uc815\uc758, \uc804\uc81c\ub85c \uc778\uc815\ud55c \uba85\uc81c, \uc774\ubbf8 \uc99d\uba85\ud55c \uc815\ub9ac, \ucd94\ub860\uaddc\uce59 \ub4f1\uc744 \ud65c\uc6a9\ud558\uc5ec \uc99d\uba85\ud558\ub294 \uac83\uc744 <span class=\"defined\">\uc5f0\uc5ed\uc801 \ucd94\ub860<\/span>\uc774\ub77c\uace0 \ud55c\ub2e4. \uc774\uc81c \uba87 \uac00\uc9c0 \ucd94\ub860\uaddc\uce59\uc744 \uc0b4\ud3b4\ubcf4\uc790.\n<\/p>\n<div class=\"theorem\">\n<p>\n\t\t<span class=\"theorem\"> Theorem 1.1.5 <\/span><br \/>\n\uc784\uc758\uc758 \uba85\uc81c \\(p, q\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ol class=\"parenthesis-roman\">\n<li> \\(p\\Longrightarrow p\\vee q\\)<span class=\"hfill\">(\ud569\uc758 \ubc95\uce59)<\/span> <\/li>\n<li> \\(p\\wedge q\\Longrightarrow p,\\quad p\\wedge q\\Longrightarrow q\\)<span class=\"hfill\"> (\ub2e8\uc21c\ud654 \ubc95\uce59)<\/span> <\/li>\n<li> \\((p\\vee q)\\wedge\\sim p\\Longrightarrow q\\)<span class=\"hfill\"> (\ub17c\ub9ac\ud569\uc0bc\ub2e8\ubc95)<\/span> <\/li>\n<\/ol>\n<\/div>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Proof.<\/span><br \/>\n\uc5ec\uae30\uc11c\ub294 (\u2172)\ub9cc \uc99d\uba85\ud55c\ub2e4. \\((p\\vee q)\\wedge\\sim p\\longrightarrow q\\)\uc758 \uc9c4\ub9ac\ud45c\ub97c \uc791\uc131\ud574\ubcf4\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<br \/>\n<img decoding=\"async\" src=\"https:\/\/coslimites.com\/wp-content\/uploads\/2020\/03\/tab-107.png\" alt=\"\" width=\"370\" height=\"\" class=\"aligncenter size-full wp-image-1936\" \/><br \/>\n\ub530\ub77c\uc11c \\((p\\vee q)\\wedge\\sim p\\Longrightarrow q\\)\uc774\ub2e4. \ub098\uba38\uc9c0 (\u2170)\uacfc (\u2171)\ub3c4 \uac19\uc740 \ubc29\ubc95\uc73c\ub85c \uc27d\uac8c \uc99d\uba85\ud560 \uc218 \uc788\ub2e4.<br \/>\n<span class=\"qed\"><\/span><\/p>\n<p>\n\uc704 \uc815\ub9ac\uc5d0\uc11c \uc0b4\ud3b4\ubcf8 \ucd94\ub860\uaddc\uce59\uc744 \uc77c\uc0c1 \uc5b8\uc5b4\ub85c \ud45c\ud604\ud558\uc5ec \uc74c\ubbf8\ud574 \ubcfc \uc218 \uc788\ub2e4. \uc608\ucee8\ub300 \uba85\uc81c \\(p\\)\ub97c &#8216;\ub098\ub294 \ub0a8\uc790\uc774\ub2e4&#8217;, \\(q\\)\ub97c &#8216;\ub098\ub294 \ud55c\uad6d\uc778\uc774\ub2e4.&#8217;\ub77c\uace0 \ud558\uba74, \uc704 \uc815\ub9ac\uc758 (\u2170)\uc758 \uba85\uc81c\ub294 &#8216;\ub098\ub294 \ub0a8\uc790\uc774\ub2e4. \ub530\ub77c\uc11c \ub098\ub294 \ub0a8\uc790\uc774\uac70\ub098 \ud55c\uad6d\uc778\uc774\ub2e4.&#8217;\uac00 \ub41c\ub2e4. \ub610\ud55c \uc704 \uc815\ub9ac\uc758 (\u2171)\uc758 \uba85\uc81c\ub294 &#8216;\ub098\ub294 \ub0a8\uc790\uc774\uace0 \ud55c\uad6d\uc778\uc774\ubbc0\ub85c \ub098\ub294 \ub0a8\uc790\uc774\ub2e4.&#8217;\uac00 \ub41c\ub2e4. \uc2e4\uc0dd\ud65c\uc5d0\uc11c\ub294 \uc0ac\uc6a9\ub418\uc9c0 \uc54a\ub294 \ud070 \uc758\ubbf8 \uc5c6\ub294 \ubb38\uc7a5\uc774\uc9c0\ub9cc \ub17c\ub9ac\uc801\uc73c\ub85c \ubcf4\uba74 \ucc38\uc774\ub2e4. \ub2e4\uc74c \ucd94\ub860\uaddc\uce59\ub4e4\ub3c4 \uc99d\uba85\uc5d0 \uc790\uc8fc \uc0ac\uc6a9\ud558\ub294 \uaddc\uce59\uc774\ub2e4.\n<\/p>\n<div class=\"theorem\">\n<p>\n\t\t<span class=\"theorem\"> Theorem 1.1.6  <\/span><br \/>\n\uc784\uc758\uc758 \ub450 \uba85\uc81c \\(p, q\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ol class=\"parenthesis-roman\">\n<li> \\(\\sim(\\sim p)\\Longleftrightarrow p\\)<span class=\"hfill\">(\uc774\uc911\ubd80\uc815\ubc95\uce59)<\/span> <\/li>\n<li> \\(p\\wedge q\\Longleftrightarrow q\\wedge p,\\quad p \\vee q\\Longleftrightarrow q\\vee p\\)<span class=\"hfill\"> (\uad50\ud658\ubc95\uce59)<\/span> <\/li>\n<li> \\(p\\wedge p\\Longleftrightarrow p,\\quad p\\vee p\\Longleftrightarrow p\\)<span class=\"hfill\"> (\uba71\ub4f1\ubc95\uce59)<\/span> <\/li>\n<li> \\((p\\longrightarrow q)\\Longleftrightarrow (\\sim q\\longrightarrow\\sim p)\\) <span class=\"hfill\"> (\ub300\uc6b0\ubc95\uce59)<\/span> <\/li>\n<\/ol>\n<\/div>\n<p>\ub2e4\uc74c\uc740 \uba85\uc81c\uc5d0 \uad00\ud55c <span class=\"defined\">\ub4dc \ubaa8\ub974\uac04\uc758 \ubc95\uce59<\/span>\uc73c\ub85c <!-- \\marginnote[.05cm]{\ub4dc \ubaa8\ub974\uac04\uc758 \ubc95\uce59\uc774 \uc5b4\ub5a4 \uc911\uc694\ud55c \uc758\ubbf8\ub97c \uac16\ub294\uac00\ub294 4\uae30 \uc774\uc885\ud604 \ud559\uc0dd\uc5d0\uac8c \ubb3c\uc5b4\ubcf4\uba74 \uc7ac\ubbf8\uc788\ub294 \uc124\uba85\uc744 \ub4e4\uc744 \uc218 \uc788\uc744 \uac83\uc774\ub2e4. (\ubb3c\ub860 \uc2dc\ud5d8\uae30\uac04 \uac19\uc740 \ubc14\uc05c \uc2dc\uae30\ub294 \ud53c\ud558\uc790.)} --><br \/>\n \ub17c\ub9ac\uc5d0\uc11c \ud3b8\ub9ac\ud55c \uc218\ub2e8\uc73c\ub85c \uc774\uc6a9\ub418\uace0 \uc788\ub294 \uc815\ub9ac\uc774\ub2e4. <\/p>\n<div class=\"theorem\">\n<p>\n\t\t<span class=\"theorem\"> Theorem 1.1.6  <\/span> (\ub4dc \ubaa8\ub974\uac04\uc758 \ubc95\uce59)<br \/>\n\ub450 \uba85\uc81c \\(p, q\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ol class=\"parenthesis-roman\">\n<li> \\(\\sim (p\\wedge q)\\Longleftrightarrow\\ \\sim p\\ \\vee \\sim q\\) <\/li>\n<li> \\(\\sim (p \\vee q)\\Longleftrightarrow\\ \\sim p\\ \\wedge \\sim q\\) <\/li>\n<\/ol>\n<\/div>\n<p>\n\uba85\uc81c &#8216;\ub098\ub294 \uac10\uc790\ub97c \uc88b\uc544\ud558\uac70\ub098 \uace0\uad6c\ub9c8\ub97c \uc88b\uc544\ud558\uac70\ub098 \ud1a0\ub9c8\ud1a0\ub97c \uc88b\uc544\ud55c\ub2e4.&#8217;\ub97c \ubd80\uc815\ud574\ubcf4\uba74 &#8216;\ub098\ub294 \uac10\uc790\ub97c \uc2eb\uc5b4\ud558\uace0 \uace0\uad6c\ub9c8\ub3c4 \uc2eb\uc5b4\ud558\uba70 \ud1a0\ub9c8\ud1a0\ub3c4 \uc2eb\uc5b4\ud55c\ub2e4.&#8217;\uac00 \ub41c\ub2e4. \ub610\ud55c, &#8216;\ub098\ub294 \ud3ad\uc218\uc774\uace0 \ud0a4\uac00 210cm \uc774\uc0c1\uc774\ub2e4.&#8217;\ub97c \ubd80\uc815\ud558\uba74 &#8216;\ub098\ub294 \ud3ad\uc218\uac00 \uc544\ub2c8\uac70\ub098 \ud0a4\uac00 210cm \ubbf8\ub9cc\uc774\ub2e4.&#8217;\uac00 \ub418\uc5b4 \ub4dc \ubaa8\ub974\uac04\uc758 \ubc95\uce59\uc774 \uc131\ub9bd\ud568\uc744 \uc74c\ubbf8\ud574 \ubcfc \uc218 \uc788\ub2e4.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 1.12 <\/span><br \/>\n\ub2e4\uc74c \uba85\uc81c\uc758 \ubd80\uc815\uc744 \ub9d0\ud558\uc5ec\ub77c.<\/p>\n<ol class=\"parenthesis\">\n<li> \ud1a0\ub07c\ub294 \ud558\uc597\uc9c0\ub3c4 \uc54a\uace0 \uadc0\uc5fd\uc9c0\ub3c4 \uc54a\ub2e4.<\/li>\n<li>  \ube44\uac00 \uc624\uba74 \uc6b0\uc0b0\uc774 \uc798 \ud314\ub9b0\ub2e4.<\/li>\n<li>  \uc560\uc778\uc774 \uc0dd\uae30\uba74 \ud559\uc5c5 \uc131\uc801\uc774 \uc88b\uc544\uc9c4\ub2e4.<\/li>\n<p> <!-- \\marginnote[-.2cm]{\\scriptsize \\sout{Vacuously true?}} --><\/p>\n<li> \ubd80\uc5c5\uc744 \ud558\uba74 \ub3c8\uc740 \ubc8c\uc9c0\ub9cc \uc5ec\uc720\ub294 \uc904\uc5b4\ub4e0\ub2e4. <\/li>\n<\/ol>\n<p>\n\ub2e4\uc74c \uc815\ub9ac\ub3c4 \ub17c\ub9ac\uc5d0 \uc788\uc5b4\uc11c \uc911\uc694\ud55c \ubc95\uce59\ub4e4\ub85c \uc774\ubbf8 \uc99d\uba85\ud588\uac70\ub098 \ud639\uc740 \uc27d\uac8c \uc99d\uba85\ud560 \uc218 \uc788\ub294 \uac83\ub4e4\uc774\ub2e4.\n<\/p>\n<div class=\"theorem\">\n<p>\n\t\t<span class=\"theorem\"> Theorem 1.1.6  <\/span> <br \/>\n\uc138 \uba85\uc81c \\(p, q, r\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ol class=\"parenthesis-roman\">\n<li> \\((p\\wedge q)\\wedge r\\ \\Longleftrightarrow\\ p\\wedge (q\\wedge r)\\)<span class=\"hfill\">(\uacb0\ud569\ubc95\uce59)<\/span> <\/li>\n<p> <!-- \\marginnote{\uacb0\ud569\ubc95\uce59\uc774\ub098 \ubd84\ubc30\ubc95\uce59 \ub4f1\uc740 \ubaa8\ub450 \uac04\ub7b5\ud788 \uc904\uc5ec \uc4f4 \ud45c\ud604\uc774\ub2e4. \uc608\ub97c \ub4e4\uc5b4 \ub17c\ub9ac\uacf1\uc758 \uacb0\ud569\ubc95\uce59, \ub17c\ub9ac\uacf1\uc758 \ub17c\ub9ac\ud569\uc5d0 \ub300\ud55c \ubd84\ubc30\ubc95\uce59\uacfc \uac19\uc774 \uc4f0\ub294 \uac83\uc774 \uc815\ud655\ud55c \ud45c\ud604\uc774\ub2e4.}--><\/p>\n<li> \\((p\\vee q)\\vee r\\ \\Longleftrightarrow\\ p\\vee(q\\vee r)\\)<span class=\"hfill\"> (\uacb0\ud569\ubc95\uce59)<\/span> <\/li>\n<li> \\(p\\wedge (q\\vee r)\\ \\Longleftrightarrow\\ (p\\wedge q)\\vee (p\\wedge r)\\)<span class=\"hfill\"> (\ubd84\ubc30\ubc95\uce59)<\/span> <\/li>\n<li>  \\(p\\vee (q\\wedge r)\\ \\Longleftrightarrow\\ (p\\vee q)\\wedge (p\\vee r)\\)<span class=\"hfill\"> (\ubd84\ubc30\ubc95\uce59)<\/span> <\/li>\n<li> \\((p\\longrightarrow q)\\wedge (q\\longrightarrow r)\\ \\Longrightarrow\\ (p\\longrightarrow r)\\)<span class=\"hfill\"> (\ucd94\uc774\ubc95\uce59)<\/span> <\/li>\n<\/ol>\n<\/div>\n<p>\n\uacb0\ud569\ubc95\uce59\uc5d0 \uc758\ud558\uc5ec<br \/>\n\\[<br \/>\n(p\\wedge q)\\wedge r\\quad\\mbox{\ud639\uc740}\\quad p\\wedge (q\\wedge r)<br \/>\n\\]<br \/>\n\uc5d0 \uc788\ub294 \uad04\ud638\ub294 \ubd88\ud544\uc694\ud558\uac8c \ub41c\ub2e4. \uc989 \\(p\\vee q\\vee r\\)\uacfc \\(p\\wedge q\\wedge r\\)\uc740 \uac01\uac01 \uc77c\uc815\ud55c \ub73b\uc744 \uc9c0\ub2cc\ub2e4. \ub9c8\ucc2c\uac00\uc9c0\ub85c \uba85\uc81c \\(p_{1}, p_{2}, \\ldots, p_{n}\\)\uc5d0 \ub300\ud558\uc5ec \\(p_{1}\\vee p_{2}\\vee \\cdots \\vee p_{n}\\)\uacfc \\(p_{1}\\wedge p_{2}\\wedge \\cdots\\wedge p_{n}\\)\uc758 \uc758\ubbf8\ub3c4 \uc790\uc5f0\uc2a4\ub7fd\uac8c \uc0dd\uac01\ud560 \uc218 \uc788\ub2e4.\n<\/p>\n<p>\n\uc9c0\uae08\uae4c\uc9c0 \uc0b4\ud3b4\ubcf8 \uc5ec\ub7ec \uac00\uc9c0 \ubc95\uce59\ub4e4\uc740 \ub2e4\uc74c\uc758 \uc608\uc81c\uc5d0\uc11c\uc640 \uac19\uc774 \ub17c\ub9ac\uc801 \ub3d9\uce58 \ubc0f \ud568\uc758\uc5d0 \ub300\ud55c \uc815\ub2f9\uc131\uc744 \uc8fc\uc7a5\ud558\ub294\ub370 \uc788\uc5b4\uc11c \ud3b8\ub9ac\ud558\uac8c \uc0ac\uc6a9\ud560 \uc218 \uc788\ub2e4. \uc774\ub978\ubc14 \ucd94\ub860\uaddc\uce59\uc774\ub77c\uace0 \ubd88\ub9ac\ub294 \uc774\ub4e4 \ubc95\uce59\uc740 \ub2e8\uc9c0 \ud3b8\ub9ac\ud558\uac8c \ud65c\uc6a9\ud558\uace0\uc790 \ud0dd\ud55c \uac83\uc77c \ubfd0 \uaddc\uce59 \uc0c1\ud638\uac04\uc758 \ub3c5\ub9bd\uc131\uc740 \uc5fc\ub450\uc5d0 \ub450\uc9c0 \uc54a\uace0 \uc788\ub2e4.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc608\uc81c 1.13 <\/span><br \/>\n\ub300\uc6b0\ubc95\uce59 \\((p\\longrightarrow q)\\ \\Leftrightarrow\\ (\\sim q\\longrightarrow\\sim p)\\)\ub97c \uc5f0\uc5ed\uc801 \ucd94\ub860\uc744 \ud1b5\ud574 \uc99d\uba85\ud558\uc5ec\ub77c.\n<\/p>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Sol.<\/span><br \/>\n\\((p\\longrightarrow q)\\ \\Leftrightarrow\\ (\\sim p\\ \\vee q)\\ \\Leftrightarrow\\ (q\\ \\vee\\sim p)\\ \\Leftrightarrow\\ [\\sim(\\sim p)\\vee (\\sim p)] \\ \\Leftrightarrow\\ \\sim q\\longrightarrow\\ \\sim p\\)<br \/>\n<span class=\"qed\"><\/span><\/p>\n<p>\n\uc870\uac74\uba85\uc81c \\(p\\longrightarrow q\\)\uc5d0\uc11c \\(p\\)\ub97c <span class=\"defined\">\uac00\uc815<\/span>\uc774\ub77c\uace0 \ud558\uace0 \\(q\\)\ub97c <span class=\"defined\">\uacb0\ub860<\/span>\uc774\ub77c\uace0 \ud558\ub294\ub370, \uac00\uc815\uacfc \uacb0\ub860\uc758 \uc704\uce58\ub97c \ubc14\uafbc \\(q\\longrightarrow p\\)\ub97c \\(p\\longrightarrow q\\)\uc758 <span class=\"defined\">\uc5ed<\/span>\uc774\ub77c\uace0 \ud55c\ub2e4. \uadf8\ub9ac\uace0 \uac00\uc815\uacfc \uacb0\ub860\uc744 \ubd80\uc815\ud55c \uc870\uac74\ubb38 \\(\\sim p\\longrightarrow\\ \\sim q\\) \ub97c \\(p\\longrightarrow q\\)\uc758 <span class=\"defined\">\uc774<\/span>\ub77c\uace0 \ud55c\ub2e4. \ub610\ud55c, \uac00\uc815\uacfc \uacb0\ub860\uc744 \ubd80\uc815\ud558\uace0 \uc5ed\uc744 \ucde8\ud55c \uc870\uac74\ubb38 \\(\\sim q\\longrightarrow\\ \\sim p\\)\ub97c \\(p\\longrightarrow q\\)\uc758 <span class=\"defined\">\ub300\uc6b0<\/span>\ub77c\uace0 \ud55c\ub2e4. \uc870\uac74\uba85\uc81c\uc758 \uc5ed, \uc774, \ub300\uc6b0 \uc0ac\uc774\uc758 \uad00\uacc4\ub97c \uadf8\ub9bc\uc73c\ub85c \ud45c\ud604\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<br \/>\n<img decoding=\"async\" src=\"https:\/\/coslimites.com\/wp-content\/uploads\/2020\/03\/fig-108.png\" alt=\"\" width=\"450\" height=\"\" class=\"aligncenter size-full wp-image-1936\" \/>\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 1.14 <\/span><br \/>\n\ub2e4\uc74c \uba85\uc81c\ub97c \uc99d\uba85\ud558\uc5ec\ub77c. (\uc9c4\ub9ac\ud45c\ub97c \uc0ac\uc6a9\ud574\ub3c4 \uc88b\uace0, \uc5f0\uc5ed\uc801\uc73c\ub85c \uc99d\uba85\ud574\ub3c4 \uc88b\ub2e4.)<\/p>\n<ol class=\"parenthesis\">\n<li> \\((p\\longrightarrow q)\\ \\Longrightarrow\\ (p\\vee r \\longrightarrow q\\vee r) \\) <\/li>\n<li> \\((p\\longleftrightarrow q)\\ \\Longrightarrow\\ (p\\wedge q)\\vee(\\sim p\\ \\wedge \\sim q) \\) <\/li>\n<li> \\(\\sim(p\\wedge q\\wedge r)\\ \\Longleftrightarrow\\ \\sim p\\ \\vee \\sim q\\ \\vee \\sim r \\) <\/li>\n<li> \\(\\sim (p\\vee q\\vee r)\\ \\Longleftrightarrow\\ \\sim p\\ \\wedge \\sim q\\ \\wedge \\sim r \\) <\/li>\n<li> \\((p\\vee q)\\ \\wedge\\sim p\\ \\Longrightarrow q\\) <\/li>\n<li> \\((p\\longrightarrow q)\\wedge (p\\longrightarrow r)\\ \\Longleftrightarrow\\ (p\\longrightarrow q\\wedge r)\\) <\/li>\n<li> \\((p\\longrightarrow q)\\ \\Longleftrightarrow\\ (p\\ \\wedge\\sim q\\ \\longrightarrow\\ q\\ \\wedge\\sim q)\\) <\/li>\n<\/ol>\n<p>\n\uc55e\uc11c \uc608\uc81c 1.13\uc5d0\uc11c \uc0b4\ud3b4\ubcf8 \ubc14\uc640 \uac19\uc774 \uc5b4\ub5a0\ud55c \uba85\uc81c\uc640 \uadf8 \ub300\uc6b0\ub294 \uc11c\ub85c \ub3d9\uce58\uc774\ub2e4. \uba85\uc81c \\(p\\longrightarrow q\\)\uac00 \ucc38\uc784\uc744 \uc99d\uba85\ud558\ub294 \ub300\uc2e0, &#8216;\\(p\\)\ub294 \ucc38\uc774\uace0 \\(q\\)\ub294 \uac70\uc9d3\uc774\ub77c\uace0 \ud558\uba74 \ubaa8\uc21c\uc774\ub2e4.&#8217;\ub294 \uac83\uc744 \ubcf4\uc774\uae30\ub3c4 \ud55c\ub2e4. \uc77c\uc0c1\uc5b8\uc5b4\ub85c \uc0dd\uac01\ud558\uba74 \ub9e4\uc6b0 \ub2f9\uc5f0\ud55c \ub17c\ub9ac\uc774\uc9c0\ub9cc, \ud615\uc2dd\uc801\uc73c\ub85c\ub294<br \/>\n\\[<br \/>\n(p\\longrightarrow q)\\ \\Longleftrightarrow\\ [ \\sim(p\\longrightarrow q)\\longrightarrow c]\\ \\Longleftrightarrow\\ (p\\ \\wedge\\sim q)\\longrightarrow c<br \/>\n\\]<br \/>\n\uc640 \uac19\uc774 \uc124\uba85\ud560 \uc218 \uc788\ub2e4. <span id='easy-footnote-2-4345' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-02\/#easy-footnote-bottom-2-4345' title=' \uc5ec\uae30\uc11c \\(c\\)\ub294 \ubaa8\uc21c\uba85\uc81c.'><sup>2<\/sup><\/a><\/span><br \/>\n \ube44\uc2b7\ud558\uac8c<br \/>\n\\[<br \/>\np\\ \\Longleftrightarrow\\ p\\vee c\\ \\Longleftrightarrow\\ \\sim p\\longrightarrow c<br \/>\n\\]<br \/>\n\ub97c \uc774\uc6a9\ud558\uc5ec, \uba85\uc81c \\(p\\)\uac00 \ucc38\uc784\uc744 \uc99d\uba85\ud558\ub294 \ub300\uc2e0, &#8216;\\(p\\)\uac00 \uac70\uc9d3\uc774\uba74 \ubaa8\uc21c\uc774\ub2e4.&#8217;\ub77c\ub294 \uac83\uc744 \ubcf4\uc774\uae30\ub3c4 \ud55c\ub2e4. \uc774\uac19\uc740  \uc99d\uba85 \ubc29\ubc95\uc744 <span class=\"defined\">\uac04\uc811\uc99d\uba85\ubc95<\/span> \ud639\uc740 <span class=\"defined\">\uadc0\ub958\ubc95<\/span>\uc774\ub77c\uace0 \ud55c\ub2e4.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc608\uc81c 1.15  <\/span><br \/>\n\uc790\uc5f0\uc218 \\(n\\)\uc5d0 \ub300\ud558\uc5ec, \\(n^2\\)\uc774 \uc9dd\uc218\uc774\uba74 \\(n\\)\ub3c4 \uc9dd\uc218\uc784\uc744 \ubcf4\uc5ec\ub77c.\n<\/p>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Sol.<\/span><br \/>\n\uc99d\uba85\ud558\uace0\uc790 \ud558\ub294 \uba85\uc81c\uc758 \ub300\uc6b0, \uc989<br \/>\n\\[<br \/>\n\\mbox{\\(n\\)\uc774 \ud640\uc218\uc774\uba74 \\(n^{2}\\)\uc740 \ud640\uc218\uc774\ub2e4.}<br \/>\n\\]<br \/>\n\ub97c \ubcf4\uc774\uba74 \ub41c\ub2e4. \\(n\\)\uc774 \ud640\uc218\uc774\uba74, \\(n=2k-1\\ (k\\in \\mathbb{N})\\)\ub85c \ub458 \uc218 \uc788\ub2e4. \uc774\ub54c<br \/>\n\\[<br \/>\nn^{2}=(2k-1)^{2}=2(2k^{2}-2k)+1<br \/>\n\\]<br \/>\n\uc774\ubbc0\ub85c \\(n^{2}\\)\ub3c4 \ud640\uc218\uc774\ub2e4.<br \/>\n<span class=\"qed\"><\/span> <\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 1.16  <\/span><br \/>\n\\(\\sqrt{2}\\)\uac00 \ubb34\ub9ac\uc218\uc784\uc744 \ubcf4\uc5ec\ub77c. <span id='easy-footnote-3-4345' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-02\/#easy-footnote-bottom-3-4345' title=' \uc7ac\ubbf8\uc0bc\uc544 \\(\\sqrt[3]{2}\\)\uac00 \ubb34\ub9ac\uc218\uc778 \uac83\ub3c4 \ubcf4\uc5ec\ubcf4\uc544\ub77c.'><sup>3<\/sup><\/a><\/span>\n<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/coslimites.com\/wp-content\/uploads\/2020\/03\/fig-109.png\" alt=\"\" width=\"170\" height=\"\" class=\"aligncenter size-full wp-image-1936\" \/><\/p>\n<p><!-- \n% \\begin{prob} \ub2e4\uc74c \uba85\uc81c\ub97c \uc9c4\ub9ac\ud45c\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc99d\uba85\ud558\uc5ec\ub77c. \\begin{enumerate}[label=(\\arabic*)] \\item \\)(p\\longrightarrow q)\\ \\Longrightarrow\\ (p\\vee r \\longrightarrow q\\vee r) \\) \\item \\)(p\\longleftrightarrow q)\\ \\Longrightarrow\\ (p\\wedge q)\\vee(\\sim p\\ \\wedge \\sim q) \\) \\item \\)\\sim(p\\wedge q\\wedge r)\\ \\Longleftrightarrow\\ \\sim p\\ \\vee \\sim q\\ \\vee \\sim r \\) \\item \\)\\sim (p\\vee q\\vee r)\\ \\Longleftrightarrow\\ \\sim p\\ \\wedge \\sim q\\ \\wedge \\sim r \\) \\end{enumerate} \\end{prob}\n--><\/p>\n<h3> \uc9d1\ud569\uc758 \uc5f0\uc0b0 <\/h3>\n<p>\n\uc9d1\ud569\uc5d0\uc11c\uc758 \uc5f0\uc0b0\uc774\ub780 \uae30\uc874\uc758 \uc9d1\ud569\uc73c\ub85c \uc0c8\ub85c\uc6b4 \ud558\ub098\uc758 \uc9d1\ud569\uc744 \uad6c\uc131\ud558\ub294 \uac83\uc744 \ub73b\ud55c\ub2e4. \uc9d1\ud569\uc758 \uc5f0\uc0b0 \uc911 \uac00\uc7a5 \uae30\ubcf8\uc774 \ub418\ub294 \uc774\ud56d\uc5f0\uc0b0(binary operation)\uc744 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.\n<\/p>\n<div class=\"definition\">\n<p>\n\t\t<span class=\"definition\"> Definition 1.1.9 <\/span><br \/>\n\uc804\uccb4\uc9d1\ud569 \\(U\\)\uc758 \ub450 \ubd80\ubd84\uc9d1\ud569 \\(A, B\\)\uc5d0 \ub300\ud558\uc5ec<\/p>\n<ol class=\"parenthesis-roman\">\n<!-- %\\item \\)\\mbox{'\\)A\\)\uc640 \\)B\\)\uc758 \ud569\uc9d1\ud569'}\\stackrel{\\text{\uae30\ud638}}{=}A\\cup B\\stackrel{\\text{\uc815\uc758}}{=}\\{ x\\in U\\mid x\\in A\\ \\vee\\ x\\in B\\} \\) --><\/p>\n<li> \\(A\\)\uc640 \\(B\\)\uc758 <span class=\"defined\">\ud569\uc9d1\ud569<\/span>:  \\(A\\cup B=\\{ x\\in U\\mid x\\in A\\ \\vee\\ x\\in B\\} \\) <\/li>\n<li> \\(A\\)\uc640 \\(B\\)\uc758 <span class=\"defined\">\uad50\uc9d1\ud569<\/span>: \\(A\\cap B=\\{ x\\in U\\mid x\\in A\\ \\wedge\\ x\\in B\\}\\) <\/li>\n<li> \\(A\\)\uc5d0 \ub300\ud55c \\(B\\)\uc758 <span class=\"defined\">\ucc28\uc9d1\ud569<\/span>: \\(A-B=\\{ x\\in U\\mid x\\in A\\ \\wedge\\ x\\not\\in B\\}\\) <\/li>\n<\/ol>\n<\/div>\n<p>\n\ub450 \uc9d1\ud569 \\(A, B\\)\uc5d0 \ub300\ud558\uc5ec, \uc774\ub4e4 \ub450 \uc9d1\ud569\uc5d0 \uacf5\ud1b5\uc73c\ub85c \uc18d\ud558\ub294 \uc6d0\uc18c\uac00 \ud558\ub098\ub3c4 \uc5c6\uc744 \ub54c, \uc989<br \/>\n\\[<br \/>\nA\\cap B=\\varnothing<br \/>\n\\]<br \/>\n\uc77c \ub54c, \uc9d1\ud569 \\(A\\)\uc640 \uc9d1\ud569 \\(B\\)\ub294 <span class=\"defined\">\uc11c\ub85c\uc18c<\/span>(disjoint)\ub77c\uace0 \ud55c\ub2e4.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 1.17  <\/span><br \/>\n\uc9d1\ud569 \\(\\{ x\\mid \\mbox{\\(x\\)\ub294 \\(3\\leq x\\leq 6\\)\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc790\uc5f0\uc218}\\}\\)\uc758 \uc9c4\ubd80\ubd84\uc9d1\ud569 \uc911 \uc9d1\ud569 \\(\\{2, 3, 4\\}\\)\uc640 \uc11c\ub85c\uc18c\uc778 \uac83\uc744 \ubaa8\ub450 \uad6c\ud558\uc5ec\ub77c.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 1.18  <\/span><br \/>\n\uc9d1\ud569 \\(\\{a, b, c, d\\}\\)\uc758 \ubd80\ubd84\uc9d1\ud569 \\(X\\)\uc5d0 \ub300\ud558\uc5ec \\(c\\in X\\)\uc774\uace0 \\(\\{a, e\\}\\)\uc640 \uc11c\ub85c\uc18c\uc778 \uc9d1\ud569 \\(X\\)\ub97c \ubaa8\ub450 \uad6c\ud558\uc5ec\ub77c.\n<\/p>\n<p>\n\ub450 \uc720\ud55c\uc9d1\ud569 \\(A, B\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[<br \/>\nn(A\\cup B)=n(A)+n(B)-n(A\\cap B)<br \/>\n\\]<br \/>\n\uac00 \uc131\ub9bd\ud568\uc744 \uc54c \uc218 \uc788\ub2e4. \ub610\ud55c \\(A, B\\)\uac00 \uc11c\ub85c\uc18c\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740  \\(n(A\\cup B)=n(A)+n(B)\\)\uc778 \uac83\ub3c4 \ud655\uc778 \ud560 \uc218 \uc788\ub2e4.\n<\/p>\n<p>\n\ud55c\ud3b8 \uc9d1\ud569\uc758 \uc774\ub860\uc5d0\uc11c \uc790\uc8fc \uc0ac\uc6a9\ud558\ub294 \ub2e4\uc74c\uc758 \uc77c\ud56d\uc5f0\uc0b0(unary operation)\ub3c4 \uc788\ub2e4.\n<\/p>\n<div class=\"definition\">\n<p>\n\t\t<span class=\"definition\"> Definition 1.1.10 <\/span><br \/>\n\uc804\uccb4\uc9d1\ud569 \\(U\\)\uc758 \ubd80\ubd84\uc9d1\ud569 \\(A\\)\uc5d0 \ub300\ud558\uc5ec \\(A\\)\uc758 <span class=\"defined\">\uc5ec\uc9d1\ud569<\/span> \\(A^{\\mathrm{C}}\\)\ub97c<br \/>\n\\[<br \/>\nA^{\\mathrm{C}}=\\{ x\\in U\\mid x\\not\\in A\\}<br \/>\n\\]<br \/>\n\ub85c \uc815\uc758\ud55c\ub2e4.\n<\/p>\n<\/div>\n<p>\n\uc774 \uc815\uc758\ub85c\ubd80\ud130<br \/>\n\\[<br \/>\nA-B=A\\cap B^{\\mathrm{C}}<br \/>\n\\]<br \/>\n\uac00 \uc131\ub9bd\ud568\uc744 \uc54c \uc218 \uc788\ub2e4. \ub610\ud55c \uc870\uac74 \\(p\\)\uc758 \uc9c4\ub9ac\uc9d1\ud569\uc774 \\(P\\)\ub77c\uba74 \\(\\sim p\\)\uc758 \uc9c4\ub9ac\uc9d1\ud569\uc740 \\(P^{\\mathrm{C}}\\)\uac00 \ub41c\ub2e4. \uc5ec\uc9d1\ud569\uacfc \uad00\ub828\ud558\uc5ec \ub2e4\uc74c\uc774 \uc131\ub9bd\ud568\uc744 \uc54c \uc218 \uc788\ub2e4.\n<\/p>\n<div class=\"theorem\">\n<p>\n\t\t<span class=\"theorem\"> Theorem 1.1.11   <\/span> (\uc5ec\uc9d1\ud569\uc758 \uc131\uc9c8) <br \/>\n\uc804\uccb4\uc9d1\ud569 \\(U\\)\uc640 \\(U\\)\uc758 \ubd80\ubd84\uc9d1\ud569 \\(A\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ol class=\"parenthesis-roman\">\n<li> \\(\\varnothing^{\\mathrm{C}}=U,\\quad U^{\\mathrm{C}}=\\varnothing\\) <\/li>\n<li> \\(A\\cup A^{\\mathrm{C}}=U,\\quad A\\cap A^{\\mathrm{C}}=\\varnothing\\) <\/li>\n<li> \\((A^{\\mathrm{C}})^{\\mathrm{C}}=A\\) <\/li>\n<\/ol>\n<\/div>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Proof.<\/span><br \/>\n\uc5ec\uae30\uc11c\ub294 (\u2172)\ub9cc \uc99d\uba85\ud55c\ub2e4.<br \/>\n\\[<br \/>\nx\\in (A^{\\mathrm{C}})^{\\mathrm{C}}\\ \\Longleftrightarrow\\ \\sim(x\\in A^{\\mathrm{C}})\\ \\Longleftrightarrow\\ \\sim(\\sim (x\\in A))\\ \\Longleftrightarrow\\ x\\in A<br \/>\n\\]<br \/>\n\uc774\ubbc0\ub85c \uc6d0\ud558\ub294 \uacb0\uacfc\ub97c \uc5bb\ub294\ub2e4.<br \/>\n<span class=\"qed\"><\/span> <\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 1.19   <\/span><br \/>\n\uc815\ub9ac 1.1.11\uc758 \ub098\uba38\uc9c0 \ub4f1\uc2dd\ub4e4\uc744 \uc99d\uba85\ud558\uc5ec\ub77c.\n<\/p>\n<p>\n\ud569\uc9d1\ud569\uacfc \uad50\uc9d1\ud569\uc740 \ub2e4\uc74c\uacfc \uac19\uc740 \uc131\uc9c8\ub4e4\uc744 \uac16\ub294\ub2e4.\n<\/p>\n<div class=\"theorem\">\n<p>\n\t\t<span class=\"theorem\"> Theorem 1.1.12  <\/span> (\ud569\uc9d1\ud569\uacfc \uad50\uc9d1\ud569\uc758 \uc131\uc9c8) <br \/>\n\uc804\uccb4\uc9d1\ud569 \\(U\\)\uc640 \\(U\\)\uc758 \ubd80\ubd84\uc9d1\ud569 \\(A, B, C\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ol class=\"parenthesis-roman\">\n<li> \\(A\\cup \\varnothing=A,\\quad A\\cap \\varnothing =\\varnothing\\) <\/li>\n<li> \\(A\\cup A=A,\\quad A\\cap A=A\\)<span class=\"hfill\"> (\uba71\ub4f1\ubc95\uce59)<\/span><\/li>\n<li> \\(A\\cup (B\\cup C)=(A\\cup B)\\cup C,\\)  \n<p>\\( A\\cap(B\\cap C)=(A\\cap B)\\cap C\\)<span class=\"hfill\">(\uacb0\ud569\ubc95\uce59)<\/span> <\/li>\n<li> \\(A\\cup B=B\\cup A,\\quad A\\cap B=B\\cap A\\)<span class=\"hfill\"> (\uad50\ud658\ubc95\uce59)<\/span> <\/li>\n<li> \\(A\\cap (B\\cup C)=(A\\cap B)\\cup (A\\cap C),\\) \n<p>\\( A\\cup(B\\cap C)=(A\\cup B)\\cap (A\\cup C)\\)<span class=\"hfill\"> (\ubd84\ubc30\ubc95\uce59)<\/span> <\/li>\n<li> \\((A\\cup B)^{\\mathrm{C}}=A^{\\mathrm{C}}\\cap B^{\\mathrm{C}},\\) \n<p>\\( (A\\cap B)^{\\mathrm{C}}=A^{\\mathrm{C}}\\cup B^{\\mathrm{C}}\\)<span class=\"hfill\">(\ub4dc \ubaa8\ub974\uac04\uc758 \ubc95\uce59)<\/span> <\/li>\n<\/ol>\n<\/div>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Proof.<\/span><br \/>\n\ub4dc \ubaa8\ub974\uac04\uc758 \ubc95\uce59 \\((A\\cup B)^{\\mathrm{C}}=A^{\\mathrm{C}}\\cap B^{\\mathrm{C}}\\)\ub9cc \uc99d\uba85\ud55c\ub2e4.<br \/>\n\\begin{align*}<br \/>\nx\\in (A\\cup B)^{\\mathrm{C}}\\ &#038;\\Longleftrightarrow\\ \\sim (x\\in A\\ \\vee\\ x\\in B) \\\\<br \/>\n&#038; \\Longleftrightarrow\\ (x\\not\\in A)\\wedge (x\\not\\in B) \\\\<br \/>\n&#038; \\Longleftrightarrow\\ (x\\in A^{\\mathrm{C}})\\wedge (x\\in B^{\\mathrm{C}}) \\\\<br \/>\n&#038; \\Longleftrightarrow\\ x\\in A^{\\mathrm{C}}\\cap B^{\\mathrm{C}}<br \/>\n\\end{align*}<br \/>\n\uc774\ubbc0\ub85c \uc6d0\ud558\ub294 \uacb0\uacfc\ub97c \uc5bb\ub294\ub2e4.<br \/>\n<span class=\"qed\"><\/span><\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 1.20   <\/span><br \/>\n\uc815\ub9ac 1.1.12\uc758 \ub098\uba38\uc9c0 \ub4f1\uc2dd\ub4e4\uc744 \uc99d\uba85\ud558\uc5ec\ub77c.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 1.21   <\/span><br \/>\n\uc804\uccb4\uc9d1\ud569 \\(U\\)\uc758 \ubd80\ubd84\uc9d1\ud569 \\(A, B, C\\)\uc5d0 \ub300\ud558\uc5ec \uc9d1\ud569\uc758 \uc5f0\uc0b0\ubc95\uce59\uc744 \uc774\uc6a9\ud558\uc5ec \ub4f1\uc2dd<br \/>\n\\[<br \/>\n(A-B)\\cap (A\\cap C^{\\mathrm{C}})=A-(B\\cup C)<br \/>\n\\]<br \/>\n\uac00 \uc131\ub9bd\ud568\uc744 \ubcf4\uc5ec\ub77c.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 1.22   <\/span><br \/>\n\uc804\uccb4\uc9d1\ud569 \\(U=\\{ 1, 2, \\ldots, 10\\}\\)\uc758 \ub450 \ubd80\ubd84\uc9d1\ud569 \\(A, B\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[<br \/>\nA=\\{ 3, 5, 10\\},\\quad A^{\\mathrm{C}}\\cap B^{\\mathrm{C}}=\\{ 1, 4, 6, 8\\}<br \/>\n\\]<br \/>\n\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc9d1\ud569 \\(B\\)\uc758 \uac1c\uc218\ub97c \uad6c\ud558\uc5ec\ub77c.\n<\/p>\n<h3> \ud55c\uc815\uaddc\uce59 <\/h3>\n<h4> &#8216;\ubaa8\ub4e0&#8217;\uc774\ub098 &#8216;\uc5b4\ub5a4&#8217;\uc774 \uc788\ub294 \uba85\uc81c <\/h4>\n<p>\n\uc77c\ubc18\uc801\uc73c\ub85c \uc870\uac74 \\(p(x)\\)\ub294 \\(x\\)\uc758 \uac12\uc774 \ubb34\uc5c7\uc774\ub0d0\uc5d0 \ub530\ub77c \ucc38, \uac70\uc9d3\uc774 \ud310\ubcc4\ub41c\ub2e4. \uadf8\ub7ec\ub098 \\(x\\)\uc55e\uc5d0 &#8216;\ubaa8\ub4e0&#8217;\uc774\ub098 &#8216;\uc5b4\ub5a4&#8217;\uacfc \uac19\uc740 \ud55c\uc815\uc220\uc0ac(quantifier)\ub97c \uc774\uc6a9\ud574 \\(x\\)\uc758 \uac12\uc758 \ubc94\uc704\ub97c \uc815\ud574\uc8fc\uba74 \uadf8 \uc9c4\uc704\uac00 \ud310\ubcc4\ub418\uc5b4 \uba85\uc81c\uac00 \ub41c\ub2e4. \uc608\ub97c \ub4e4\uc5b4<br \/>\n\\[<br \/>\n\\mbox{\ubaa8\ub4e0 \uc2e4\uc218 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(x^{2}\\geq 0\\)}<br \/>\n\\]<br \/>\n\uc740 \ucc38\uc778 \uba85\uc81c\uc774\uace0<br \/>\n\\[<br \/>\n\\mbox{\uc5b4\ub5a4 \uc2e4\uc218 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(x^{2}=-1\\)}<br \/>\n\\]<br \/>\n\uc740 \uac70\uc9d3\uc778 \uba85\uc81c\uc774\ub2e4.\n<\/p>\n<p>\n\uc804\uccb4\uc9d1\ud569 \\(U\\)\uc5d0\uc11c \uc815\uc758\ub41c \uc870\uac74 \\(p(x)\\)\uc758 \uc9c4\ub9ac\uc9d1\ud569\uc744 \\(P\\)\ub77c\uace0 \ud560 \ub54c, \uba85\uc81c<br \/>\n\\[<br \/>\n\\mbox{\ubaa8\ub4e0 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(p(x)\\)}<br \/>\n\\]<br \/>\n\ub294 \\(P=U\\)\uc774\uba74 \ucc38\uc774\uace0, \\(P\\neq U\\)\uc774\uba74 \uac70\uc9d3\uc774\ub2e4.<span id='easy-footnote-4-4345' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-02\/#easy-footnote-bottom-4-4345' title='&amp;#8216;\ubaa8\ub4e0&amp;#8217;\uc744 &amp;#8216;\uc784\uc758\uc758&amp;#8217;\ub85c \ubc14\uafb8\uc5b4 \uc368\ub3c4 \uac19\uc740 \ub73b\uc774 \ub41c\ub2e4.'><sup>4<\/sup><\/a><\/span> \ub610\ud55c \uba85\uc81c<br \/>\n\\[<br \/>\n\\mbox{\uc5b4\ub5a4 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(p(x)\\)}<br \/>\n\\]<br \/>\n\ub294 \\(P\\neq\\varnothing\\)\uc774\uba74 \ucc38\uc774\uace0 \\(P=\\varnothing\\)\uc774\uba74 \uac70\uc9d3\uc774\ub2e4.<\/p>\n<p>\n\ud55c\uc815\uc220\uc0ac\uac00 \ud3ec\ud568\ub41c \uba85\uc81c\ub97c \uae30\ud638\ub97c \uc774\uc6a9\ud574 \ub354 \uac04\ub2e8\ud788 \uc4f0\uae30\ub3c4 \ud55c\ub2e4. \ubcf4\ud1b5 \uba85\uc81c<br \/>\n\\[<br \/>\n\\mbox{\ubaa8\ub4e0 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(p(x)\\)}<br \/>\n\\]<br \/>\n\ub97c \uac04\ub2e8\ud788<br \/>\n\\[<br \/>\n(\\forall x) (p(x))<br \/>\n\\]<br \/>\n\ub85c \ub098\ud0c0\ub0b4\uace0, \uba85\uc81c<br \/>\n\\[<br \/>\n\\mbox{\uc5b4\ub5a4 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(p(x)\\)}<br \/>\n\\]<br \/>\n\ub97c \uac04\ub2e8\ud788 <span id='easy-footnote-5-4345' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-02\/#easy-footnote-bottom-5-4345' title='\uba85\uc81c &amp;#8216;\uc5b4\ub5a4 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(p(x)\\)&amp;#8217;\ub294 \uba85\uc81c &amp;#8216;\\(p(x)\\)\uc778 \\(x\\)\uac00 \uc874\uc7ac\ud55c\ub2e4.&amp;#8217;\uc640 \ub3d9\uc77c\ud55c \ub9d0\uc774\ub2e4.'><sup>5<\/sup><\/a><\/span><br \/>\n\\[<br \/>\n(\\exists x)(p(x))<br \/>\n\\]<br \/>\n\ub85c \ub098\ud0c0\ub0b8\ub2e4.  \ucc38\uace0\ub85c \\(\\forall\\)\uc740 All\uc758 A\ub97c \uac70\uafb8\ub85c \uc4f4 \uac83\uc774\uace0 \\(\\exists\\)\ub294 Exists\uc758 E\ub97c \uac70\uafb8\ub85c \uc4f4 \uac83\uc774\ub2e4.\n<\/p>\n<h4> \ud55c\uc815\uae30\ud638\uc758 \ubd80\uc815 <\/h4>\n<p>\n\uc870\uac74 \\(p(x)\\)\uc758 \uc9c4\ub9ac\uc9d1\ud569\uc774 \\(P\\)\ub77c\uace0 \ud558\uc790. \uba85\uc81c<br \/>\n\\[<br \/>\n\\mbox{\uc5b4\ub5a4 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(p(x)\\)}<br \/>\n\\]<br \/>\n\uc758 \ub73b\uc740 \\(P\\neq \\varnothing\\)\uacfc \ub3d9\uc77c\ud558\ubbc0\ub85c \uc774\ub97c \ubd80\uc815\ud558\uba74 \\(P=\\varnothing\\)\uc774\ub2e4. \uc989 \\(P^{\\mathrm{C}}=U\\)\ub77c\ub294 \ub73b\uc774\ub2e4. \uc774\ub97c \ub2e4\uc2dc \ud45c\ud604\ud558\uba74<br \/>\n\\[<br \/>\nU=P^{\\mathrm{C}}=\\{ x\\mid\\ \\sim p(x)\\}<br \/>\n\\]<br \/>\n\uc774\ubbc0\ub85c \uba85\uc81c<br \/>\n\\[<br \/>\n\\mbox{\ubaa8\ub4e0 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(\\sim p(x)\\)}<br \/>\n\\]<br \/>\n\ub85c \uc4f8 \uc218 \uc788\ub2e4. \ub530\ub77c\uc11c \ub2e4\uc74c\uc758 \ub450 \uba85\uc81c<br \/>\n\\[<br \/>\n\\sim [\\mbox{\uc5b4\ub5a4 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(p(x)\\)}],\\quad \\mbox{\ubaa8\ub4e0 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(\\sim p(x)\\)}<br \/>\n\\]<br \/>\n\ub294 \ub17c\ub9ac\uc801\uc73c\ub85c \ub3d9\uce58\uc774\ub2e4. \ub9c8\ucc2c\uac00\uc9c0\ub85c \ub2e4\uc74c\uc758 \ub450 \uba85\uc81c<br \/>\n\\[<br \/>\n\\sim [\\mbox{\ubaa8\ub4e0 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(p(x)\\)}],\\quad \\mbox{\uc5b4\ub5a4 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(\\sim p(x)\\)}<br \/>\n\\]<br \/>\n\ub3c4 \ub17c\ub9ac\uc801\uc73c\ub85c \ub3d9\uce58\uc784\uc744 \uc54c \uc218 \uc788\ub2e4.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 1.23   <\/span><br \/>\n\ub2e4\uc74c \uba85\uc81c\uc758 \ubd80\uc815\uc744 \ub9d0\ud558\uc5ec\ub77c.<\/p>\n<ol class=\"parenthesis\">\n<li> \ubaa8\ub4e0 \uc0ac\ub78c\uc740 \uba38\ub9ac\uac00 \uc788\ub2e4. <\/li>\n<li> \uc6b0\ub9ac \ubc18 \ud559\uc0dd\uc740 \ubaa8\ub450 \uc5ec\ud559\uc0dd\uc774\ub2e4. <\/li>\n<li> \uba38\ub9ac\uce74\ub77d\uc774 \ud558\uc580 \uc0ac\ub78c\ub3c4 \uc788\ub2e4. <\/li>\n<li> \ud574\uc0b0\ubb3c\uc744 \uba39\uc9c0 \ubabb\ud558\ub294 \uc0ac\ub78c\uc774 \uc788\ub2e4. <\/li>\n<li> \ud734\ub300\uc804\ud654\ub97c \uc18c\uc720\ud558\uc9c0 \uc54a\uc740 \uc0ac\ub78c\uc740 \uc5c6\ub2e4. <\/li>\n<li> \ub204\uad6c\ub098 \uc778\ud130\ub137\uc744 \ud560 \uc904 \uc548\ub2e4.\n<\/ol>\n<\/p>\n<hr>\n","protected":false},"excerpt":{"rendered":"<p>\uc5f0\uc5ed\uc801 \ucd94\ub860 \ub450 \uc870\uac74 \\(p, q\\)\uc5d0 \ub300\ud558\uc5ec, \ubb38\uc7a5 &#8216;\\(p\\longrightarrow q\\)&#8217;\ub294 \ud558\ub098\uc758 \uba85\uc81c\uac00 \ub41c\ub2e4. \uc77c\ubc18\uc801\uc73c\ub85c \uc870\uac74 \\(p, q\\)\uc758 \uc9c4\ub9ac\uc9d1\ud569\uc744 \uac01\uac01 \\(P, Q\\)\ub77c \ud560 \ub54c, \\(p\\longrightarrow q\\)\uac00 \ucc38\uc774\uba74 \uc870\uac74 \\(p\\)\ub97c \ucc38\uc774\ub418\uac8c \ud558\ub294 \uc6d0\uc18c\ub294 \uc870\uac74 \\(q\\)\ub3c4 \ucc38\uc774 \ub418\uac8c \ud558\ubbc0\ub85c \\(P\\subset Q\\)\uc778 \uad00\uacc4\uac00 \uc131\ub9bd\ud55c\ub2e4. \ub610\ud55c \\(P\\subset Q\\)\uc778 \uad00\uacc4\uac00 \uc788\uc73c\uba74 \uba85\uc81c \\(p\\longrightarrow q\\)\ub294 \ucc38\uc774\ub2e4. \ud55c\ud3b8, \uba85\uc81c \\(p\\longrightarrow q\\)\uac00 \uac70\uc9d3\uc774\ub77c\ub294 \uac83\uc740 \uc870\uac74 \\(p\\)\uac00 \ucc38\uc774 \ub418\uc9c0\ub9cc \\(q\\)\ub294 \ucc38\uc774 \ub418\uc9c0 \uc54a\ub294 \uc6d0\uc18c\uac00&hellip;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"categories":[54],"tags":[371,372,378,380,102,379],"class_list":["post-4345","post","type-post","status-publish","format-standard","hentry","category-basic-mathematics","tag-371","tag-372","tag-378","tag-380","tag-102","tag-379"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/4345","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=4345"}],"version-history":[{"count":5,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/4345\/revisions"}],"predecessor-version":[{"id":4399,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/4345\/revisions\/4399"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=4345"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/categories?post=4345"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/tags?post=4345"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}