{"id":9250,"date":"2025-10-17T19:43:49","date_gmt":"2025-10-17T10:43:49","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=9250"},"modified":"2025-10-20T18:48:32","modified_gmt":"2025-10-20T09:48:32","slug":"ch04-relations-and-functions","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/invitation-to-mathematical-logic\/ch04-relations-and-functions\/","title":{"rendered":"\uad00\uacc4\uc640 \ud568\uc218"},"content":{"rendered":"<div class=\"mathlogic2025\"><!-- ################## --><\/p>\n<p><!-- \n\n<h2>4. \uad00\uacc4\uc640 \ud568\uc218<\/h2>\n\n --><\/p>\n<p>\uc218\ud559\uc5d0\uc11c <span class=\"defined\">\uad00\uacc4<\/span>(relation)\ub294 \uc9d1\ud569\uc758 \uc6d0\uc18c\ub4e4 \uc0ac\uc774\uc758 \uc5f0\uacb0 \uc5ec\ubd80\ub97c \ub098\ud0c0\ub0b4\ub294 \uac1c\ub150\uc774\ub2e4. \ud568\uc218\ub294 \ud2b9\ubcc4\ud55c \uc885\ub958\uc758 \uad00\uacc4\ub85c\uc11c, \uc218\ud559\uc758 \uac70\uc758 \ubaa8\ub4e0 \ubd84\uc57c\uc5d0\uc11c \ud575\uc2ec\uc801\uc778 \uc5ed\ud560\uc744 \ud55c\ub2e4. \uc774 \uc7a5\uc5d0\uc11c\ub294 \uad00\uacc4\uc640 \ud568\uc218\uc758 \uc815\uc758\uc640 \uae30\ubcf8 \uc131\uc9c8\uc744 \uc0b4\ud3b4\ubcf8\ub2e4.<\/p>\n<h3>1. \uad00\uacc4\uc758 \uc815\uc758<\/h3>\n<p>\uc9d1\ud569 \\(A\\)\uc640 \\(B\\)\uc5d0 \ub300\ud558\uc5ec, \\(A\\)\uc5d0\uc11c \\(B\\)\ub85c\uc758 <span class=\"defined\">\uad00\uacc4<\/span>(relation) \\(R\\)\uc740 \ub370\uce74\ub974\ud2b8 \uacf1 \\(A \\times B\\)\uc758 \ubd80\ubd84\uc9d1\ud569\uc774\ub2e4. \uc989,<br \/>\n\\[R \\subseteq A \\times B\\]<br \/>\n\uc77c\ub54c \\(R\\)\uc744 \\(A\\)\uc5d0\uc11c \\(B\\)\ub85c\uc758 \uad00\uacc4\ub77c\uace0 \ubd80\ub978\ub2e4. \\((a,\\, b) \\in R\\)\uc77c \ub54c, &#8220;\\(a\\)\uc640 \\(b\\) \uc0ac\uc774\uc5d0 \\(R\\)-\uad00\uacc4\uac00 \uc788\ub2e4&#8221; \ub610\ub294 &#8220;\\(a\\)\uc640 \\(b\\)\uac00 \uad00\uacc4 \\(R\\)\uc5d0 \uc788\ub2e4&#8221;\ub77c\uace0 \ub9d0\ud55c\ub2e4. \uc774\uac83\uc744 \\(aRb\\)\ub85c \ub098\ud0c0\ub0b4\uae30\ub3c4 \ud55c\ub2e4.<\/p>\n<p>\ud2b9\ud788 \\(A = B\\)\uc778 \uacbd\uc6b0, \\(R \\subseteq A \\times A\\)\ub97c \\(A\\) \uc704\uc758 \uad00\uacc4\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<p>\uc608\ub97c \ub4e4\uc5b4, \\(A = \\{1,\\, 2,\\, 3\\}\\)\uc77c \ub54c, &#8220;\uc791\uac70\ub098 \uac19\ub2e4&#8221; \uad00\uacc4\ub97c \uc6d0\uc18c\ub098\uc5f4\ubc95\uc73c\ub85c \ub098\ud0c0\ub0b4\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<br \/>\n\\[R = \\{(1,\\,1),\\, (1,\\,2),\\, (1,\\,3),\\, (2,\\,2),\\, (2,\\,3),\\, (3,\\,3)\\}.\\]<\/p>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 4.1.<\/span><br \/>\n\ub2e4\uc74c \uad00\uacc4\ub97c \uc6d0\uc18c\ub098\uc5f4\ubc95\uc73c\ub85c \ub098\ud0c0\ub0b4\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(A\\)\uac00 \\(10\\) \uc774\ud558\uc778 \uc591\uc758 \uc815\uc218\uc758 \ubaa8\uc784\uc774\uace0, \\((n,\\,m)\\in R\\)\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc744 &#8220;\\(n\\)\uc774 \\(m\\)\uc758 \uc57d\uc218\uc774\ub2e4&#8221;\ub77c\uace0 \uc815\uc758\ud588\uc744 \ub54c, \uad00\uacc4 \\(R\\).<\/li>\n<li>\\(A\\)\uac00 \\(10\\) \uc774\ud558\uc778 \uc591\uc758 \uc815\uc218\uc758 \ubaa8\uc784\uc774\uace0, \\((n,\\,m)\\in E\\)\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc744 &#8220;\\(n\\)\uacfc \\(m\\)\uc758 \uacf5\uc57d\uc218\uc758 \uac1c\uc218\uac00 \\(2\\)\uc774\ub2e4&#8221;\ub77c\uace0 \uc815\uc758\ud588\uc744 \ub54c, \uad00\uacc4 \\(E\\).<\/li>\n<li>\\(\\mathbb{Z}\\)\uac00 \uc815\uc218 \uc804\uccb4\uc758 \uc9d1\ud569\uc774\uace0, \\(n\\equiv m\\)\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc744 &#8220;\\(n\\)\uc744 \\(4\\)\ub85c \ub098\ub208 \ub098\uba38\uc9c0\uc640 \\(m\\)\uc744 \\(4\\)\ub85c \ub098\ub208 \ub098\uba38\uc9c0\uac00 \uac19\ub2e4&#8221;\ub77c\uace0 \uc815\uc758\ud588\uc744 \ub54c, \uad00\uacc4 \\(\\equiv\\).<\/li>\n<li>\\(\\mathbb{N}\\)\uc774 \uc591\uc758 \uc815\uc218 \uc804\uccb4 \uc9d1\ud569\uc774\uace0, \\(x\\)\uc640 \\(y\\)\uac00 \\(y=x^2\\)\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uac83\uc744 \\(xRy\\)\ub85c \ub098\ud0c0\ub0bc \ub54c, \uad00\uacc4 \\(R\\).<\/li>\n<\/ol>\n<\/div>\n<p>\uad00\uacc4 \\(R \\subseteq A \\times B\\)\uc758 \uc815\uc758\uc5ed\uacfc \uce58\uc5ed\uc744 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<\/p>\n<ul>\n<li><span class=\"defined\">\uc815\uc758\uc5ed<\/span>(domain): \\(\\text{dom}(R) = \\{a \\in A \\mid \\exists b \\in B : (a,\\,b) \\in R\\}.\\)<\/li>\n<li><span class=\"defined\">\uce58\uc5ed<\/span>(range): \\(\\text{ran}(R) = \\{b \\in B \\mid \\exists a \\in A : (a,\\,b) \\in R\\}.\\)<\/li>\n<\/ul>\n<h3>2. \ud569\uc131\uad00\uacc4\uc640 \uc5ed\uad00\uacc4<\/h3>\n<p>\uad00\uacc4 \\(R \\subseteq A \\times B\\)\uc640 \\(S \\subseteq B \\times C\\)\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, <span class=\"defined\">\ud569\uc131\uad00\uacc4<\/span>(composite relation) \\(S \\circ R\\)\uc744 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<br \/>\n\\[S \\circ R = \\{(a,\\, c) \\in A \\times C \\mid \\exists b \\in B : (a,\\,b) \\in R \\,\\text{ and }\\, (b,\\,c) \\in S\\}.\\]<br \/>\n\uad00\uacc4 \\(R \\subseteq A \\times B\\)\uc758 <span class=\"defined\">\uc5ed\uad00\uacc4<\/span>(inverse relation) \\(R^{-1}\\)\ub97c \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<br \/>\n\\[R^{-1} = \\{(b,\\, a) \\in B \\times A \\mid (a,\\,b) \\in R\\}.\\]<\/p>\n<div class=\"problem\">\n<p><span class=\"problem\">\ubb38\uc81c 4.2.<\/span><br \/>\n\ud569\uc131\uad00\uacc4\uc640 \uc5ed\uad00\uacc4\ub294 \uc5b8\uc81c \uc815\uc758\ub418\ub294\uac00? \uc989, \uc8fc\uc5b4\uc9c4 \uad00\uacc4\uac00 \uc5b4\ub5a4 \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0ac \ub54c \ud569\uc131\uad00\uacc4\uc640 \uc5ed\uad00\uacc4\ub97c \uc815\uc758\ud560 \uc218 \uc788\ub294\uac00?<\/p>\n<\/div>\n<p>\uad00\uacc4\uc758 \ud569\uc131\uc5d0 \ub300\ud558\uc5ec \uacb0\ud569\ubc95\uce59\uc774 \uc131\ub9bd\ud55c\ub2e4. \uc989, \\(R \\subseteq A \\times B\\), \\(S \\subseteq B \\times C\\), \\(T \\subseteq C \\times D\\)\uc77c \ub54c, \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<br \/>\n\\[(T \\circ S) \\circ R = T \\circ (S \\circ R)\\]<br \/>\n\ub610\ud55c \uc5ed\uad00\uacc4\uc640 \uad00\ub828\ud558\uc5ec \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ul>\n<li>\\((R^{-1})^{-1} = R\\)<\/li>\n<li>\\((S \\circ R)^{-1} = R^{-1} \\circ S^{-1}\\)<\/li>\n<li>\\(\\text{dom}(R^{-1}) = \\text{ran}(R)\\)<\/li>\n<li>\\(\\text{ran}(R^{-1}) = \\text{dom}(R)\\)<\/li>\n<\/ul>\n<div class=\"problem\">\n<p><span class=\"problem\">\ubb38\uc81c 4.3.<\/span><br \/>\n\uc704 \ub4f1\uc2dd\uc744 \uc99d\uba85\ud558\uc2dc\uc624.<\/p>\n<\/div>\n<div class=\"problem\">\n<p><span class=\"problem\">\ubb38\uc81c 4.4.<\/span><br \/>\n\uad00\uacc4\uc758 \ud569\uc131\uc758 \uacb0\ud569\ubc95\uce59\uc744 \uc99d\uba85\ud558\uc2dc\uc624.<\/p>\n<\/div>\n<h3>3. \uad00\uacc4\uc758 \uc885\ub958<\/h3>\n<p>\\(R\\)\uc774 \uc9d1\ud569 \\(A\\) \uc704\uc758 \uad00\uacc4\ub77c\uace0 \ud558\uc790. \uc989 \\(R \\subseteq A \\times A\\)\ub77c\uace0 \ud558\uc790. \uc774\ub54c \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<\/p>\n<ul>\n<li>\\(R\\)\uc774 <span class=\"defined\">\ubc18\uc0ac\uc801<\/span>(reflexive) \uad00\uacc4\ub77c \ud568\uc740, \ubaa8\ub4e0 \\(a \\in A\\)\uc5d0 \ub300\ud574 \\((a,\\, a) \\in R\\)\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uac83\uc744 \uc758\ubbf8\ud55c\ub2e4.<\/li>\n<li>\\(R\\)\uc774 <span class=\"defined\">\ub300\uce6d\uc801<\/span>(symmetric) \uad00\uacc4\ub77c \ud568\uc740, \\((a,\\, b) \\in R\\)\uc77c \ub54c\ub9c8\ub2e4 \\((b,\\, a) \\in R\\)\uc774 \uc131\ub9bd\ud558\ub294 \uac83\uc744 \uc758\ubbf8\ud55c\ub2e4.<\/li>\n<li>\\(R\\)\uc774 <span class=\"defined\">\ubc18\ub300\uce6d\uc801<\/span>(antisymmetric) \uad00\uacc4\ub77c \ud568\uc740, \\((a,\\, b) \\in R\\)\uc774\uace0 \\((b,\\, a) \\in R\\)\uc77c \ub54c\ub9c8\ub2e4 \\(a = b\\)\uac00 \uc131\ub9bd\ud558\ub294 \uac83\uc744 \uc758\ubbf8\ud55c\ub2e4.<\/li>\n<li>\\(R\\)\uc774 <span class=\"defined\">\ucd94\uc774\uc801<\/span>(transitive) \uad00\uacc4\ub77c \ud568\uc740, \\((a,\\, b) \\in R\\)\uc774\uace0 \\((b,\\, c) \\in R\\)\uc77c \ub54c\ub9c8\ub2e4 \\((a,\\, c) \\in R\\)\uc774 \uc131\ub9bd\ud558\ub294 \uac83\uc744 \uc758\ubbf8\ud55c\ub2e4.<\/li>\n<\/ul>\n<p>\ud2b9\ud788 \uc218\ud559\uc5d0\uc11c \uc911\uc694\ud55c \uc5ed\ud560\uc744 \ud558\ub294 \uad00\uacc4\ub294 \ub3d9\uce58\uad00\uacc4\uc640 \uc21c\uc11c\uad00\uacc4\uc774\ub2e4.<\/p>\n<ul>\n<li>\ubc18\uc0ac\uc801\uc774\uace0 \ub300\uce6d\uc801\uc774\uba70 \ucd94\uc774\uc801\uc778 \uad00\uacc4\ub97c <span class=\"defined\">\ub3d9\uce58\uad00\uacc4<\/span>(equivalence relation)\ub77c\uace0 \ubd80\ub978\ub2e4.<\/li>\n<li>\ubc18\uc0ac\uc801\uc774\uace0 \ubc18\ub300\uce6d\uc801\uc774\uba70 \ucd94\uc774\uc801\uc778 \uad00\uacc4\ub97c <span class=\"defined\">\uc21c\uc11c\uad00\uacc4<\/span>(order relation)\ub77c\uace0 \ubd80\ub978\ub2e4.<\/li>\n<\/ul>\n<h3>4. \uad00\uacc4\uc758 \uc608<\/h3>\n<p>\uc218\ud559\uc5d0\uc11c \uc790\uc8fc \ub4f1\uc7a5\ud558\ub294 \uad00\uacc4\uc758 \uc608\ub97c \uc0b4\ud3b4\ubcf4\uc790.<\/p>\n<ul>\n<li>\uc2e4\uc218 \uc9d1\ud569\uc5d0\uc11c\uc758 \ub4f1\ud638 \uad00\uacc4: \\(R = \\{(x,\\, x) \\mid x \\in \\mathbb{R}\\}\\)\ub294 \ub3d9\uce58\uad00\uacc4\uc774\ub2e4.<\/li>\n<li>\uc2e4\uc218 \uc9d1\ud569\uc5d0\uc11c\uc758 \ubd80\ub4f1\ud638 \uad00\uacc4: \\(R = \\{(x,\\, y) \\mid x \\leq y\\}\\)\ub294 \uc21c\uc11c\uad00\uacc4\uc774\ub2e4.<\/li>\n<li>\uc9d1\ud569\uc871\uc5d0\uc11c\uc758 \ubd80\ubd84\uc9d1\ud569 \uad00\uacc4: \uc9d1\ud569\uc871 \\(\\mathcal{F}\\)\uc5d0 \ub300\ud574 \\(R = \\{(A,\\, B) \\mid A \\subseteq B\\}\\)\ub294 \uc21c\uc11c\uad00\uacc4\uc774\ub2e4.<\/li>\n<li>\uc815\uc218 \uc9d1\ud569\uc5d0\uc11c\uc758 \ud569\ub3d9 \uad00\uacc4: \uc591\uc758 \uc815\uc218 \\(n\\)\uc5d0 \ub300\ud574 \\(R = \\{(a,\\, b) \\mid a \\equiv b \\pmod{n}\\}\\)\uc740 \ub3d9\uce58\uad00\uacc4\uc774\ub2e4.<\/li>\n<li>\uc591\uc758 \uc815\uc218 \uc9d1\ud569\uc5d0\uc11c\uc758 \uc57d\uc218 \uad00\uacc4: \\(R = \\{(a,\\, b) \\mid a \\text{\ub294 } b\\text{\uc758 \uc57d\uc218}\\}\\)\ub294 \uc21c\uc11c\uad00\uacc4\uc774\ub2e4.<\/li>\n<\/ul>\n<div class=\"problem\">\n<p><span class=\"problem\">\ubb38\uc81c 4.5.<\/span><br \/>\n\uc704 \uc608\uc5d0\uc11c \uc0b4\ud3b4\ubcf8 \uad00\uacc4\uac00 \uac01\uac01 \ub3d9\uce58\uad00\uacc4 \ub610\ub294 \uc21c\uc11c\uad00\uacc4\uc758 \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0b4\uc744 \ud655\uc778\ud558\uc2dc\uc624.<\/p>\n<\/div>\n<div class=\"problem\">\n<p><span class=\"problem\">\ubb38\uc81c 4.6.<\/span><br \/>\n\\(S\\)\uac00 \uc9d1\ud569\ub4e4\uc758 \ubaa8\uc784\uc774\ub77c\uace0 \ud558\uc790. (\ubaa8\ub4e0 \uc9d1\ud569\uc758 \ubaa8\uc784\uc774\ub77c\ub294 \ub73b\uc740 \uc544\ub2c8\ub2e4.) \uc774\ub54c \uc9d1\ud569\uc758 \ub300\ub4f1\uad00\uacc4(\uc6d0\uc18c\uc758 \uac1c\uc218\uac00 \uac19\uc740 \uad00\uacc4)\ub294 \\(S\\) \uc704\uc758 \ub3d9\uce58\uad00\uacc4\uc784\uc744 \uc99d\uba85\ud558\uc2dc\uc624.<\/p>\n<\/div>\n<div class=\"problem\">\n<p><span class=\"problem\">\ubb38\uc81c 4.7.<\/span><br \/>\n\\(\\mathcal{V}\\)\uac00 \uc2e4\ubca1\ud130\uacf5\uac04\ub4e4\uc758 \ubaa8\uc784\uc774\ub77c\uace0 \ud558\uc790. \uc774\ub54c \ub3d9\ud615 \uad00\uacc4\ub294 \\(\\mathcal{V}\\) \uc704\uc758 \ub3d9\uce58\uad00\uacc4\uc784\uc744 \uc99d\uba85\ud558\uc2dc\uc624.<\/p>\n<\/div>\n<div class=\"problem\">\n<p><span class=\"problem\">\ubb38\uc81c 4.8.<\/span><br \/>\n\uc9d1\ud569\uc758 &#8216;<span class=\"defined\">\ubd84\ud560<\/span>&#8216;(partition)\uc758 \uc815\uc758\ub97c \ucc3e\uc544\ubcf4\uace0, \ubd84\ud560\uacfc \ub3d9\uce58\uad00\uacc4\uac00 \uc5b4\ub5a0\ud55c \uad00\uacc4\uac00 \uc788\ub294\uc9c0 \ud0d0\uad6c\ud558\uc2dc\uc624.<\/p>\n<\/div>\n<h3>5. \uc81c\ud55c\ub41c \uad00\uacc4<\/h3>\n<p>\uad00\uacc4 \\(R \\subseteq A \\times A\\)\uc640 \ubd80\ubd84\uc9d1\ud569 \\(B \\subseteq A\\)\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \\(R\\)\uc758 \uc815\uc758\uc5ed\uc774 \\(B\\)\ub85c <span class=\"defined\">\uc81c\ud55c\ub41c \uad00\uacc4<\/span>(restriction) \\(R|_B\\)\ub97c \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<br \/>\n\\[R|_B = R \\cap (B \\times B) = \\{(x,\\, y) \\in R \\mid x,\\, y \\in B\\}.\\]<br \/>\n\uc608\ub97c \ub4e4\uc5b4, \uc2e4\uc218\uc5d0\uc11c\uc758 \uc21c\uc11c\uad00\uacc4 \\(\\leq\\)\ub97c \uc720\ub9ac\uc218 \uc9d1\ud569 \\(\\mathbb{Q}\\)\ub85c \uc81c\ud55c\ud558\uba74 \uc720\ub9ac\uc218\uc5d0\uc11c\uc758 \uc21c\uc11c\uad00\uacc4\ub97c \uc5bb\ub294\ub2e4. \uc81c\ud55c\ub41c \uad00\uacc4\ub294 \uc6d0\ub798 \uad00\uacc4\uc758 \uc131\uc9c8\uc744 \uc774\uc5b4\ubc1b\ub294\ub2e4. \uc989, \\(R\\)\uc774 \ubc18\uc0ac\uc801\uc774\uba74 \\(R|_B\\)\ub3c4 \ubc18\uc0ac\uc801\uc774\ub2e4. \ub300\uce6d\uc131\uacfc \ucd94\uc774\uc131\ub3c4 \ub9c8\ucc2c\uac00\uc9c0\ub85c \uc774\uc5b4\ubc1b\ub294\ub2e4.<\/p>\n<h3>6. \ud568\uc218\uc758 \uc815\uc758<\/h3>\n<p><span class=\"defined\">\ud568\uc218<\/span>(function) \\(f: A \\to B\\)\ub294 \ub2e4\uc74c \ub450 \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uad00\uacc4 \\(f \\subseteq A \\times B\\)\ub97c \ub73b\ud55c\ub2e4.<\/p>\n<ol class=\"parenthesis\">\n<li>\ud568\uc22b\uac12\uc758 \uc874\uc7ac\uc131: \ubaa8\ub4e0 \\(a \\in A\\)\uc5d0 \ub300\ud574, \\((a,\\, b) \\in f\\)\uc778 \\(b \\in B\\)\uac00 \uc874\uc7ac\ud55c\ub2e4.<\/li>\n<li>\ud568\uc22b\uac12\uc758 \uc720\uc77c\uc131: \\((a,\\, b) \\in f\\)\uc774\uace0 \\((a,\\, c) \\in f\\)\uc774\uba74 \\(b = c\\)\uc774\ub2e4.<\/li>\n<\/ol>\n<p>\ub2e4\uc2dc \ub9d0\ud574, \ud568\uc218\ub294 \uc815\uc758\uc5ed\uc758 \ubaa8\ub4e0 \uc6d0\uc18c\uc5d0 \ub300\ud574 \uce58\uc5ed\uc758 \uc6d0\uc18c\ub97c \uc815\ud655\ud788 \ud558\ub098\uc529 \ub300\uc751\uc2dc\ud0a4\ub294 \uad00\uacc4\uc774\ub2e4.<\/p>\n<p>\\((a,\\, b) \\in f\\)\uc77c \ub54c, \\(b\\)\ub97c \\(a\\)\uc758 <span class=\"defined\">\uc0c1<\/span>(image) \ub610\ub294 \\(f\\)\uc5d0 \uc758\ud55c \\(a\\)\uc758 <span class=\"defined\">\ud568\uc22b\uac12<\/span>\uc774\ub77c\uace0 \ubd80\ub974\uace0 \\(f(a) = b\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n<p>\ud568\uc218 \\(f: A \\to B\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<\/p>\n<ul>\n<li>\\(A\\)\ub97c \\(f\\)\uc758 <span class=\"defined\">\uc815\uc758\uc5ed<\/span>(domain)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/li>\n<li>\\(B\\)\ub97c \\(f\\)\uc758 <span class=\"defined\">\uacf5\uc5ed<\/span>(codomain)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/li>\n<li>\\(\\{y\\in B \\mid y=f(x) \\text{ for some } x\\in A \\} \\subseteq B\\)\ub97c \\(f\\)\uc758 <span class=\"defined\">\uce58\uc5ed<\/span>(range)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/li>\n<\/ul>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 4.9.<\/span><br \/>\n\uc9d1\ud569 \\(A\\), \\(B\\)\uc640 \uad00\uacc4 \\(R\\)\uc774 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ub418\uc5b4 \uc788\uc744 \ub54c, \\(R\\)\uc774 \\(A\\)\ub85c\ubd80\ud130 \\(B\\)\ub85c\uc758 \ud568\uc218\uac00 \ub418\ub294\uc9c0 \ud310\ubcc4\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(A\\)\uc640 \\(B\\)\uac00 \uc2e4\uc218 \uc804\uccb4 \uc9d1\ud569\uc774\uace0, \\((x,\\,y)\\in R\\)\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \\(x=y^2\\)\uc774\ub2e4.<\/li>\n<li>\\(A\\)\uc640 \\(B\\)\uac00 \uc591\uc758 \uc2e4\uc218 \uc804\uccb4\uc758 \uc9d1\ud569\uc774\uace0, \\((x,\\,y)\\in R\\)\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \\(x=y^2\\)\uc774\ub2e4.<\/li>\n<li>\\(A\\)\uc640 \\(B\\)\uac00 \uc591\uc758 \uc815\uc218 \uc804\uccb4 \uc9d1\ud569\uc774\uace0, \\((p,\\,q)\\in R\\)\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \\(p\\)\uac00 \\(q\\)\uc758 \uc57d\uc218\uc778 \uac83\uc774\ub2e4.<\/li>\n<li>\\(A\\)\uc640 \\(B\\)\uac00 \uc591\uc758 \uc815\uc218 \uc804\uccb4 \uc9d1\ud569\uc774\uace0, \\((p,\\,q)\\in R\\)\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \\(12\\)\uc640 \\(p\\)\uc758 \ucd5c\uc18c\uacf5\ubc30\uc218\uac00 \\(q\\)\uc778 \uac83\uc774\ub2e4.<\/li>\n<\/ol>\n<\/div>\n<h3>7. \ud568\uc218\uc758 \uc885\ub958<\/h3>\n<p>\ud568\uc218 \\(f: A \\to B\\)\ub97c \uc6d0\uc18c\uc758 \ub300\uc751 \uc591\uc0c1\uc5d0 \ub530\ub77c \ub2e4\uc74c\uacfc \uac19\uc774 \ubd84\ub958\ud55c\ub2e4.<\/p>\n<ul>\n<li><span class=\"defined\">\uc77c\ub300\uc77c\ud568\uc218<\/span>(one-to-one): \\(f\\)\uac00 &#8220;\\(f(a_1) = f(a_2)\\)\uc774\uba74 \\(a_1 = a_2\\)\uc774\ub2e4&#8221;\ub97c \ub9cc\uc871\uc2dc\ud0a8\ub2e4.<\/li>\n<li><span class=\"defined\">\uc704\ub85c\uc758 \ud568\uc218<\/span>(onto): \\(f\\)\uac00 &#8220;\ubaa8\ub4e0 \\(b \\in B\\)\uc5d0 \ub300\ud574, \\(f(a) = b\\)\uc778 \\(a \\in A\\)\uac00 \uc874\uc7ac\ud55c\ub2e4&#8221;\ub97c \ub9cc\uc871\uc2dc\ud0a8\ub2e4.<\/li>\n<li><span class=\"defined\">\uc77c\ub300\uc77c\ub300\uc751<\/span>(one-to-one correspondence): \\(f\\)\uac00 \uc77c\ub300\uc77c\ud568\uc218\uc774\uba74\uc11c \uc704\ub85c\uc758 \ud568\uc218\uc774\ub2e4.[\uc77c\ub300\uc77c\ud568\uc218, \uc704\ub85c\uc758 \ud568\uc218, \uc77c\ub300\uc77c\ub300\uc751\uc744 \uac01\uac01 \ub2e8\uc0ac\ud568\uc218(injective function), \uc804\uc0ac\ud568\uc218(surjective function), \uc804\ub2e8\uc0ac\ud568\uc218(bijective function)\ub77c\uace0 \ubd80\ub974\uae30\ub3c4 \ud55c\ub2e4.]<\/li>\n<\/ul>\n<p>\uc608\ub97c \ub4e4\uc5b4 \ub2e4\uc74c\uacfc \uac19\uc740 \ud568\uc218\ub97c \uc0b4\ud3b4\ubcf4\uc790.<\/p>\n<ul>\n<li>\\(f: \\mathbb{R} \\to \\mathbb{R}\\), \\(f(x) = x^2\\)\uc740 \uc77c\ub300\uc77c\ud568\uc218\ub3c4 \uc544\ub2c8\uace0 \uc704\ub85c\uc758 \ud568\uc218\ub3c4 \uc544\ub2c8\ub2e4.<\/li>\n<li>\\(f: [0,\\, \\infty) \\to \\mathbb{R}\\), \\(f(x) = x^2\\)\uc740 \uc77c\ub300\uc77c\ud568\uc218\uc774\uc9c0\ub9cc \uc704\ub85c\uc758 \ud568\uc218\ub294 \uc544\ub2c8\ub2e4.<\/li>\n<li>\\(f: \\mathbb{R} \\to [0,\\, \\infty)\\), \\(f(x) = x^2\\)\uc740 \uc704\ub85c\uc758 \ud568\uc218\uc774\uc9c0\ub9cc \uc77c\ub300\uc77c\ud568\uc218\ub294 \uc544\ub2c8\ub2e4.<\/li>\n<li>\\(f: \\mathbb{R} \\to \\mathbb{R}\\), \\(f(x) = 2x + 1\\)\uc740 \uc77c\ub300\uc77c\ub300\uc751\uc774\ub2e4.<\/li>\n<\/ul>\n<p>\uc704 \uc608\uc5d0\uc11c \ubcf4\ub2e4\uc2dc\ud53c, \uac19\uc740 \uc2dd\uc744 \uc0ac\uc6a9\ud558\uc5ec \uc815\uc758\ub41c \ud568\uc218\uc77c\uc9c0\ub77c\ub3c4 \uc815\uc758\uc5ed\uc774\ub098 \uacf5\uc5ed\uc774 \ub2e4\ub974\uba74 \ub2e4\ub978 \ud568\uc218\uc774\ub2e4.<\/p>\n<div class=\"problem\">\n<p><span class=\"problem\">\ubb38\uc81c 4.10.<\/span><br \/>\n<span class=\"defined\">\uc81c\ud55c\ud568\uc218<\/span>(restriction)\uc640 <span class=\"defined\">\ud655\uc7a5\ud568\uc218<\/span>(extension)\uc758 \uac1c\ub150\uc744 \uc870\uc0ac\ud574 \ubcf4\uc790.<\/p>\n<\/div>\n<h3>8. \ud568\uc218\uc758 \ud569\uc131\uacfc \uc5ed\ud568\uc218<\/h3>\n<p>\ud568\uc218 \\(f: A \\to B\\)\uc640 \\(g: B \\to C\\)\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ud569\uc131\uad00\uacc4 \\(g\\circ f\\)\ub294 \ud568\uc218\uac00 \ub418\uae30 \uc704\ud55c \ub450 \uc870\uac74\uc744 \ubaa8\ub450 \ub9cc\uc871\uc2dc\ud0a8\ub2e4. \uc774\ub54c \\(g\\circ f : A \\rightarrow C\\)\ub97c \\(f\\)\uc640 \\(g\\)\uc758 <span class=\"defined\">\ud569\uc131\ud568\uc218<\/span>(composite function)\ub77c\uace0 \ubd80\ub978\ub2e4. \ud569\uc131\ud568\uc218\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \uc2dd\uc73c\ub85c \uc815\uc758\ud560 \uc218\ub3c4 \uc788\ub2e4.<br \/>\n\\[(g \\circ f)(a) = g(f(a)) \\quad \\text{for all }\\, a \\in A .\\]<br \/>\n\ud568\uc218\uc758 \ud569\uc131\uc5d0 \ub300\ud558\uc5ec \uacb0\ud569\ubc95\uce59\uc774 \uc131\ub9bd\ud55c\ub2e4. \uc989 \ub2e4\uc74c \ub4f1\uc2dd\uc774 \uc131\ub9bd\ud55c\ub2e4.<br \/>\n\\[(h \\circ g) \\circ f = h \\circ (g \\circ f).\\]<br \/>\n\ud568\uc218 \\(f: A \\to B\\)\uac00 \uc77c\ub300\uc77c\ub300\uc751\uc77c \ub54c, \uc5ed\uad00\uacc4 \\(f^{-1}\\)\ub294 \ud568\uc218\uac00 \ub418\uae30 \uc704\ud55c \ub450 \uc870 \uac74\uc744 \ubaa8\ub450 \ub9cc\uc871\uc2dc\ud0a8\ub2e4. \uc774\ub54c \\(f^{-1}\\)\ub97c \\(f\\)\uc758 <span class=\"defined\">\uc5ed\ud568\uc218<\/span>(inverse function)\ub77c\uace0 \ubd80\ub978\ub2e4. \uc5b4\ub5a4 \ud568\uc218\uc758 \uc5ed\ud568\uc218\uac00 \uc874\uc7ac\ud560 \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \uadf8 \ud568\uc218\uac00 \uc77c\ub300\uc77c\ub300\uc751\uc778 \uac83\uc774\ub2e4.<\/p>\n<p>\uc5b4\ub5a4 \ud568\uc218\uc758 \uc5ed\ud568\uc218\uac00 \uc874\uc7ac\ud560 \ub54c, \ud568\uc218\uc640 \uadf8 \uc5ed\ud568\uc218\uc758 \ud569\uc131\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n<ul>\n<li>\\(f^{-1} \\circ f = \\text{id}_A\\) (\uc5ec\uae30\uc11c \\(\\text{id}_A\\)\ub294 \\(A\\)\uc758 \ud56d\ub4f1\ud568\uc218)<\/li>\n<li>\\(f \\circ f^{-1} = \\text{id}_B\\)<\/li>\n<\/ul>\n<h3>9. \ud568\uc218\uc640 \uad00\ub828\ub41c \uc815\ub9ac\ub4e4<\/h3>\n<p>\ud568\uc218\uc758 \ud569\uc131\uacfc \uad00\ub828\ud558\uc5ec \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ul>\n<li>\\(f: A \\to B\\), \\(g: B \\to C\\)\uac00 \ubaa8\ub450 \uc77c\ub300\uc77c\ud568\uc218\uc774\uba74 \\(g \\circ f\\)\ub3c4 \uc77c\ub300\uc77c\ud568\uc218\uc774\ub2e4.<\/li>\n<li>\\(f: A \\to B\\), \\(g: B \\to C\\)\uac00 \ubaa8\ub450 \uc704\ub85c\uc758 \ud568\uc218\uc774\uba74 \\(g \\circ f\\)\ub3c4 \uc704\ub85c\uc758 \ud568\uc218\uc774\ub2e4.<\/li>\n<li>\\(g \\circ f\\)\uac00 \uc77c\ub300\uc77c\ud568\uc218\uc774\uba74 \\(f\\)\ub294 \uc77c\ub300\uc77c\ud568\uc218\uc774\ub2e4.<\/li>\n<li>\\(g \\circ f\\)\uac00 \uc704\ub85c\uc758 \ud568\uc218\uc774\uba74 \\(g\\)\ub294 \uc704\ub85c\uc758 \ud568\uc218\uc774\ub2e4.<\/li>\n<\/ul>\n<div class=\"problem\">\n<p><span class=\"problem\">\ubb38\uc81c 4.11.<\/span><br \/>\n\ud568\uc218\uc758 \ud569\uc131 \ubc0f \ub300\uc751\uacfc \uad00\ub828\ub41c \uc704 \uc131\uc9c8\uc744 \uc99d\uba85\ud558\uc2dc\uc624.<\/p>\n<\/div>\n<p>\ud568\uc218 \\(f:A \\rightarrow B\\)\uc640 \uc9d1\ud569 \\(C\\subseteq A\\) \uadf8\ub9ac\uace0 \\(D\\subseteq B\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<\/p>\n<ul>\n<li>\\(f\\)\uc5d0 \uc758\ud55c \\(C\\)\uc758 <span class=\"defined\">\uc0c1<\/span>(image): \\(f(C) = \\left\\{ f(x) \\mid x\\in C \\right\\}\\)<\/li>\n<li>\\(f\\)\uc5d0 \uc758\ud55c \\(D\\)\uc758 <span class=\"defined\">\uc5ed\uc0c1<\/span>(inverse image): \\(f^{-1} (D) = \\left\\{ x\\in A \\mid y=f(x) \\text{ for some } y\\in D \\right\\}\\)<\/li>\n<\/ul>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 4.12.<\/span><br \/>\n\\(A\\)\uc640 \\(B\\)\uac00 \uc9d1\ud569\uc774\uace0 \\(\\left\\{ A_i \\right\\}_{i\\in I}\\)\uac00 \uc9d1\ud569\uc871\uc774\uba70, \uc784\uc758\uc758 \\(i\\in I\\)\uc5d0 \ub300\ud558\uc5ec \\(A_i \\subseteq A\\)\ub97c \ub9cc\uc871\uc2dc\ud0a8\ub2e4\uace0 \ud558\uc790. \uadf8\ub9ac\uace0 \\(f:A \\rightarrow B\\)\uac00 \ud568\uc218\ub77c\uace0 \ud558\uc790. \ub2e4\uc74c\uc744 \uc99d\uba85\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis marginbottomhalf\">\n<li>\\(f\\left( \\bigcup_{i\\in I} A_i \\right) = \\bigcup_{i\\in I} f\\left( A_i \\right) \\)<\/li>\n<li>\\(f\\left( \\bigcap_{i\\in I} A_i \\right) \\subseteq \\bigcap_{i\\in I} f\\left( A_i \\right) \\)<\/li>\n<\/ol>\n<p>\ud2b9\ud788 (2)\uc5d0\uc11c \ub4f1\uc2dd\uc774 \uc131\ub9bd\ud558\uc9c0 \uc54a\ub294 \uc608\ub97c \uc81c\uc2dc\ud558\uc2dc\uc624. \ub610\ud55c \\(f\\)\uac00 \uc77c\ub300\uc77c\ud568\uc218\uc77c \ub54c\ub294 (2)\uc5d0\uc11c \ub4f1\uc2dd\uc774 \uc131\ub9bd\ud568\uc744 \uc99d\uba85\ud558\uc2dc\uc624.<\/p>\n<\/div>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 4.13.<\/span><br \/>\n\\(A\\)\uc640 \\(B\\)\uac00 \uc9d1\ud569\uc774\uace0 \\(\\left\\{ B_j \\right\\}_{j\\in J}\\)\uac00 \uc9d1\ud569\uc871\uc774\uba70, \uc784\uc758\uc758 \\(j\\in J\\)\uc5d0 \ub300\ud558\uc5ec \\(B_j \\subseteq B\\)\ub97c \ub9cc\uc871\uc2dc\ud0a8\ub2e4\uace0 \ud558\uc790. \uadf8\ub9ac\uace0 \\(f:A \\rightarrow B\\)\uac00 \ud568\uc218\ub77c\uace0 \ud558\uc790. \ub2e4\uc74c\uc744 \uc99d\uba85\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(f^{-1} \\left( \\bigcup_{j\\in J} B_j \\right) = \\bigcup_{j\\in J} f^{-1}\\left( B_j \\right) \\)<\/li>\n<li>\\(f^{-1} \\left( \\bigcap_{j\\in J} B_j \\right) = \\bigcap_{j\\in J} f^{-1}\\left( B_j \\right) \\)<\/li>\n<\/ol>\n<\/div>\n<div class=\"contentbottombox\">\n<p class=\"contentbottomboxtitle\"><a href=\"\/blog\/invitation-to-mathematical-logic\/\">\uc9d1\ud569\uacfc \uc218\ub9ac\ub17c\ub9ac \uccab\uac78\uc74c \ubaa9\ucc28 \ubcf4\uae30<\/a><\/p>\n<p><span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch01-naive-logic\/\">\uba85\uc81c\uc640 \ub17c\ub9ac<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch02-sets\">\uc9d1\ud569\uc758 \uac1c\ub150<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch03-algebra-of-classes\">\ub2e4\uc591\ud55c \uc9d1\ud569\uc758 \uc5f0\uc0b0<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch04-relations-and-functions\">\uad00\uacc4\uc640 \ud568\uc218<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch05-infinite-sets\">\uc720\ud55c\uc9d1\ud569\uacfc \ubb34\ud55c\uc9d1\ud569<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch06-natural-numbers\">\uc790\uc5f0\uc218<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch07-cardinal-numbers\">\uc9d1\ud569\uc758 \uae30\uc218<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch08-ordinal-numbers\">\uc9d1\ud569\uc758 \uc11c\uc218<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch09-axiomatic-set-theory\">\uc9d1\ud569\ub860\uc758 \uacf5\ub9ac<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch10-axiom-of-choice\">\uc120\ud0dd \uacf5\ub9ac<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch11-formal-logic\">\ud615\uc2dd\ub17c\ub9ac<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch12-propositional-logic\">\uba85\uc81c\ub17c\ub9ac\uc758 \uac1c\ub150<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch13-soundness-completeness-proplogic\">\uba85\uc81c\ub17c\ub9ac\uc758 \uac74\uc804\uc131\uacfc \uc644\uc804\uc131<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch14-syntax-first-order-logic\">\uc77c\uacc4\ub17c\ub9ac\uc758 \uad6c\ubb38\ub860<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch15-semantics-first-order-logic\">\uc77c\uacc4\ub17c\ub9ac\uc758 \uc758\ubbf8\ub860<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch16-inference-rule-first-order-logic\">\uc77c\uacc4\ub17c\ub9ac\uc758 \ucd94\ub860\uaddc\uce59<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch17-compactness-first-order-logic\">\uc77c\uacc4\ub17c\ub9ac\uc758 \ucf64\ud329\ud2b8\uc131<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch18-peano-arithmetics\">\ud398\uc544\ub178 \uc0b0\uc220<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch19-incompleteness-theorem\">\ubd88\uc644\uc804\uc131 \uc815\ub9ac<\/a><\/span>\n<\/div>\n<\/div>\n<p><!-- ################## --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\uc218\ud559\uc5d0\uc11c \uad00\uacc4(relation)\ub294 \uc9d1\ud569\uc758 \uc6d0\uc18c\ub4e4 \uc0ac\uc774\uc758 \uc5f0\uacb0 \uc5ec\ubd80\ub97c \ub098\ud0c0\ub0b4\ub294 \uac1c\ub150\uc774\ub2e4. \ud568\uc218\ub294 \ud2b9\ubcc4\ud55c \uc885\ub958\uc758 \uad00\uacc4\ub85c\uc11c, \uc218\ud559\uc758 \uac70\uc758 \ubaa8\ub4e0 \ubd84\uc57c\uc5d0\uc11c \ud575\uc2ec\uc801\uc778 \uc5ed\ud560\uc744 \ud55c\ub2e4. \uc774 \uc7a5\uc5d0\uc11c\ub294 \uad00\uacc4\uc640 \ud568\uc218\uc758 \uc815\uc758\uc640 \uae30\ubcf8 \uc131\uc9c8\uc744 \uc0b4\ud3b4\ubcf8\ub2e4. 1. \uad00\uacc4\uc758 \uc815\uc758 \uc9d1\ud569 \\(A\\)\uc640 \\(B\\)\uc5d0 \ub300\ud558\uc5ec, \\(A\\)\uc5d0\uc11c \\(B\\)\ub85c\uc758 \uad00\uacc4(relation) \\(R\\)\uc740 \ub370\uce74\ub974\ud2b8 \uacf1 \\(A \\times B\\)\uc758 \ubd80\ubd84\uc9d1\ud569\uc774\ub2e4. \uc989, \\(R \\subseteq A \\times B\\) \uc77c\ub54c \\(R\\)\uc744 \\(A\\)\uc5d0\uc11c \\(B\\)\ub85c\uc758 \uad00\uacc4\ub77c\uace0 \ubd80\ub978\ub2e4. \\((a,\\, b) \\in R\\)\uc77c \ub54c, &#8220;\\(a\\)\uc640 \\(b\\)&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":9246,"menu_order":104,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"class_list":["post-9250","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9250","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=9250"}],"version-history":[{"count":8,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9250\/revisions"}],"predecessor-version":[{"id":9399,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9250\/revisions\/9399"}],"up":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9246"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=9250"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}