{"id":5828,"date":"2022-01-26T01:12:59","date_gmt":"2022-01-26T01:12:59","guid":{"rendered":"https:\/\/www.cybermedian.com\/cn\/?p=5828"},"modified":"2026-04-20T09:13:26","modified_gmt":"2026-04-20T09:13:26","slug":"%e7%bb%b4%e6%81%a9%e5%9b%be%ef%bc%9a%e7%bb%bc%e5%90%88%e6%95%99%e7%a8%8b","status":"publish","type":"post","link":"https:\/\/www.cybermedian.com\/cn\/venn-diagram-a-comprehensive-tutorial\/","title":{"rendered":"\u7ef4\u6069\u56fe\uff1a\u7efc\u5408\u6559\u7a0b"},"content":{"rendered":"<p id=\"d482\" class=\"graf graf--p graf-after--h3\"><a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/www.visual-paradigm.com\/tutorials\/how-to-create-venn-diagram\/\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/www.visual-paradigm.com\/tutorials\/how-to-create-venn-diagram\/\">\u7ef4\u6069\u56fe<\/a>\u00a0\u662f\u4e0d\u540c\u4e8b\u7269\u7ec4\u4e4b\u95f4\u5173\u7cfb\u7684\u56fe\u5f62\u6216\u56fe\u5f62\u8868\u793a\u3002\u7ef4\u6069\u56fe\u662f\u7ea6\u7ff0\u7ef4\u6069\u5728 1880 \u5e74\u5de6\u53f3\u53d1\u660e\u7684\u3002\u7ef4\u6069\u56fe\u4e5f\u79f0\u4e3a\u96c6\u5408\u56fe\u3002\u7ef4\u6069\u56fe\u7ed9\u51fa\u4e86\u7ec4\u6216\u96c6\u5408\u7684\u903b\u8f91\u8868\u793a\u3002\u501f\u52a9\u7ef4\u6069\u56fe\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u7406\u89e3\u4e24\u4e2a\u6216\u4e09\u4e2a\u96c6\u5408\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u5728\u6570\u5b66\u4e2d\uff0c\u7ef4\u6069\u56fe\u7528\u4e8e\u5206\u6790\u4ece\u8c03\u67e5\u3001\u6570\u636e\u62a5\u544a\u548c\u8868\u683c\u4e2d\u83b7\u5f97\u7684\u5df2\u77e5\u4fe1\u606f\u3002<\/p>\n<figure id=\"6adb\" class=\"graf graf--figure graf-after--p\"><img decoding=\"async\" class=\"graf-image\" src=\"https:\/\/www.cybermedian.com\/cn\/wp-content\/uploads\/sites\/6\/2022\/02\/0jv6HuCeAN5cp2cGo.png\" data-image-id=\"0*jv6HuCeAN5cp2cGo.png\" data-width=\"523\" data-height=\"341\" data-is-featured=\"true\" \/><\/figure>\n<h3 id=\"58e8\" class=\"graf graf--h3 graf-after--figure\"><span id=\"Purpose_of_Venn_diagrams\">\u7ef4\u6069\u56fe\u7684\u76ee\u7684<\/span><\/h3>\n<ul class=\"postList\">\n<li id=\"6c5d\" class=\"graf graf--li graf-after--h3\">\u7ef4\u6069\u56fe\u53ef\u4ee5\u6709\u6548\u5730\u663e\u793a\u591a\u4e2a\u6570\u636e\u96c6\uff08\u901a\u5e38\u662f\u4e24\u5230\u56db\u4e2a\uff09\u4e4b\u95f4\u7684\u76f8\u4f3c\u4e4b\u5904\u6216\u5dee\u5f02\u3002<\/li>\n<li id=\"ac55\" class=\"graf graf--li graf-after--li\">\u7ef4\u6069\u56fe\u8fd8\u63cf\u8ff0\u4e86\u7edf\u4e00\u51e0\u4e2a\u6570\u636e\u7ec4\u7684\u7ed3\u679c\u3002<\/li>\n<li id=\"3f70\" class=\"graf graf--li graf-after--li\">\u4ed6\u4eec\u8fd8\u53ef\u4ee5\u63cf\u8ff0\u4e24\u4e2a\u7ec4\u7ec7\/\u56e2\u961f\u7684\u91cd\u53e0\u804c\u8d23\u3002<\/li>\n<\/ul>\n<h3 id=\"0478\" class=\"graf graf--h3 graf-after--li\"><span id=\"Circle_Venn_Diagrams\">\u5706\u7ef4\u6069\u56fe<\/span><\/h3>\n<p id=\"6808\" class=\"graf graf--p graf-after--h3\">\u7ef4\u6069\u56fe\u4f7f\u7528\u5706\u5708\u6765\u8868\u793a\u96c6\u5408\u5e76\u8bf4\u660e\u4e0d\u540c\u96c6\u5408\u7684\u6709\u9650\u96c6\u5408\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u5728\u6570\u5b66\u4e2d\uff0c\u7ef4\u6069\u56fe\u7528\u4e8e\u5206\u6790\u4ece\u8c03\u67e5\u3001\u6570\u636e\u62a5\u544a\u548c\u7531\u591a\u6761\u91cd\u53e0\u95ed\u5408\u66f2\u7ebf\uff08\u901a\u5e38\u662f\u5706\u5f62\uff09\u7ec4\u6210\u7684\u8868\u683c\u4e2d\u83b7\u5f97\u7684\u5df2\u77e5\u4fe1\u606f\uff0c\u6bcf\u6761\u66f2\u7ebf\u4ee3\u8868\u4e00\u4e2a\u96c6\u5408\u3002<\/p>\n<p id=\"f64b\" class=\"graf graf--p graf-after--p\">\u4f8b\u5982\uff1a<\/p>\n<ul class=\"postList\">\n<li id=\"1fbd\" class=\"graf graf--li graf-after--p\">\u81ea\u7136\u6570\u96c6 = {1,2,3,\u2026..}<\/li>\n<li id=\"9eba\" class=\"graf graf--li graf-after--li\">\u6574\u6570\u96c6 = {0,1,2,3,\u2026..}<\/li>\n<li id=\"511a\" class=\"graf graf--li graf-after--li\">\u6bcf\u4e2a\u5bf9\u8c61\u79f0\u4e3a\u96c6\u5408\u7684\u4e00\u4e2a\u5143\u7d20\u3002<\/li>\n<\/ul>\n<p id=\"2555\" class=\"graf graf--p graf-after--li\">\u4ee5\u4e0b\u793a\u4f8b\u663e\u793a\u4e86\u4e0e\u7ef4\u6069\u56fe\u76f8\u5173\u7684\u96c6\u5408\u7684\u57fa\u672c\u64cd\u4f5c\u3002<\/p>\n<p id=\"d9ac\" class=\"graf graf--p graf-after--p\"><strong class=\"markup--strong markup--p-strong\">\u96c6\u5408\u57fa\u672c\u8fd0\u7b97\u7ef4\u6069\u56fe<\/strong>\u4e24\u4e2a\u96c6\u5408 A \u2229B = \u7684\u4ea4\u96c6\u662f\u96c6\u5408 A \u548c B \u4e2d\u5b58\u5728\u7684\u5143\u7d20\u6570\u3002<\/p>\n<figure id=\"e190\" class=\"graf graf--figure graf-after--p\"><img decoding=\"async\" class=\"graf-image\" src=\"https:\/\/www.cybermedian.com\/cn\/wp-content\/uploads\/sites\/6\/2022\/02\/04Ewt8pwoo5TjwINb.png\" data-image-id=\"0*4Ewt8pwoo5TjwINb.png\" data-width=\"300\" data-height=\"190\" \/><\/figure>\n<p id=\"1e3c\" class=\"graf graf--p graf-after--figure\">\u4e24\u4e2a\u96c6\u5408\u7684\u5e76\u96c6 AUB = \u662f\u5b58\u5728\u4e8e\u96c6\u5408 A \u6216 B \u4e2d\u7684\u5143\u7d20\u7684\u6570\u91cf\u3002<\/p>\n<figure id=\"94d1\" class=\"graf graf--figure graf-after--p\"><img decoding=\"async\" class=\"graf-image\" src=\"https:\/\/www.cybermedian.com\/cn\/wp-content\/uploads\/sites\/6\/2022\/02\/04DuGQINtKO09jOL7.png\" data-image-id=\"0*4DuGQINtKO09jOL7.png\" data-width=\"300\" data-height=\"190\" \/><\/figure>\n<p id=\"2c2a\" class=\"graf graf--p graf-after--figure\">\u4e24\u4e2a\u5bf9\u79f0\u5dee<\/p>\n<figure id=\"4008\" class=\"graf graf--figure graf-after--p\"><img decoding=\"async\" class=\"graf-image\" src=\"https:\/\/www.cybermedian.com\/cn\/wp-content\/uploads\/sites\/6\/2022\/02\/0-wkmOGfahEAzl8hb.png\" data-image-id=\"0*-wkmOGfahEAzl8hb.png\" data-width=\"300\" data-height=\"190\" \/><\/figure>\n<h3 id=\"674d\" class=\"graf graf--h3 graf-after--figure\"><span id=\"Venn_Diagram_Examples\">\u7ef4\u6069\u56fe\u793a\u4f8b<\/span><\/h3>\n<h4 id=\"713b\" class=\"graf graf--h4 graf-after--h3\"><span id=\"Venn_Example_Class_of_Students\">\u7ef4\u6069\u793a\u4f8b\uff1a\u5b66\u751f\u73ed\u7ea7<\/span><\/h4>\n<p id=\"21db\" class=\"graf graf--p graf-after--h4\">\u5728\u4e00\u4e2a 100 \u4eba\u7684\u73ed\u7ea7\u4e2d\uff0c35 \u4eba\u559c\u6b22\u79d1\u5b66\uff0c45 \u4eba\u559c\u6b22\u6570\u5b66\u300210 \u4e24\u4e2a\u90fd\u559c\u6b22\u3002\u6709\u591a\u5c11\u4eba\u559c\u6b22\uff0c\u53c8\u6709\u591a\u5c11\u4eba\u90fd\u4e0d\u559c\u6b22\uff1f<\/p>\n<ul class=\"postList\">\n<li id=\"b584\" class=\"graf graf--li graf-after--p\">\u5b66\u751f\u603b\u6570\uff0cn(\u00b5) = 100<\/li>\n<li id=\"5872\" class=\"graf graf--li graf-after--li\">\u7406\u79d1\u5b66\u751f\u4eba\u6570\uff0cn(S) = 35<\/li>\n<li id=\"93f5\" class=\"graf graf--li graf-after--li\">\u6570\u5b66\u5b66\u751f\u4eba\u6570\uff0cn(M) = 45<\/li>\n<li id=\"271d\" class=\"graf graf--li graf-after--li\">\u4e24\u8005\u90fd\u559c\u6b22\u7684\u5b66\u751f\u4eba\u6570\uff0cn(M\u2229S) = 10<\/li>\n<li id=\"8052\" class=\"graf graf--li graf-after--li\">\u559c\u6b22\u5176\u4e2d\u4efb\u4f55\u4e00\u4e2a\u7684\u5b66\u751f\u4eba\u6570\uff0c<\/li>\n<li id=\"53ff\" class=\"graf graf--li graf-after--li\">n(M\u1d1cS) = n(M) + n(S) \u2014 n(M\u2229S)<\/li>\n<li id=\"53d4\" class=\"graf graf--li graf-after--li\">\u2192 45+35\u201310 = 70<\/li>\n<li id=\"8ad6\" class=\"graf graf--li graf-after--li\">\u4e0d\u559c\u6b22\u7684\u5b66\u751f\u4eba\u6570 = n(\u00b5) \u2014 n(M\u1d1cS) = 100\u201370 = 30<\/li>\n<\/ul>\n<figure id=\"fa53\" class=\"graf graf--figure graf-after--li\"><img decoding=\"async\" class=\"graf-image\" src=\"https:\/\/www.cybermedian.com\/cn\/wp-content\/uploads\/sites\/6\/2022\/02\/0vACU2FMysmXKfaQd.png\" data-image-id=\"0*vACU2FMysmXKfaQd.png\" data-width=\"584\" data-height=\"343\" \/><\/figure>\n<p id=\"cd1c\" class=\"graf graf--p graf-after--figure\"><a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/online.visual-paradigm.com\/app\/diagrams\/#diagram:proj=0&amp;type=UseCaseDiagram&amp;name=Venn-Diagram&amp;external=https%3A%2F%2Feditor.visual-paradigm.com%2Fwp-content%2Fuploads%2Fsites%2F7%2F2020%2F01%2Fvenn-diagram-class-of-students-example.png\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/online.visual-paradigm.com\/app\/diagrams\/#diagram:proj=0&amp;type=UseCaseDiagram&amp;name=Venn-Diagram&amp;external=https%3A%2F%2Feditor.visual-paradigm.com%2Fwp-content%2Fuploads%2Fsites%2F7%2F2020%2F01%2Fvenn-diagram-class-of-students-example.png\">\u7f16\u8f91\u6b64\u7ef4\u6069\u56fe<\/a><\/p>\n<h4 id=\"9a46\" class=\"graf graf--h4 graf-after--p\"><span id=\"Venn_Diagram_Example_Mammals_and_Fish\">\u7ef4\u6069\u56fe\u793a\u4f8b\uff1a\u54fa\u4e73\u52a8\u7269\u548c\u9c7c\u7c7b<\/span><\/h4>\n<p id=\"b9c5\" class=\"graf graf--p graf-after--h4\">\u8fd9\u662f\u4e00\u4e2a\u7ef4\u6069\u56fe\u793a\u4f8b\uff0c\u663e\u793a\u4e86\u54fa\u4e73\u52a8\u7269\u548c\u9c7c\u7c7b\u7684\u7279\u5f81\uff0c\u5b83\u4eec\u88ab\u5206\u7ec4\u4e3a\u4e24\u4e2a\u692d\u5706\u3002\u5171\u540c\u7684\u7279\u5f81\u88ab\u653e\u7f6e\u5728\u4e24\u4e2a\u692d\u5706\u7684\u91cd\u53e0\u533a\u57df\u5185\u3002<\/p>\n<figure id=\"8b60\" class=\"graf graf--figure graf-after--p\"><img decoding=\"async\" class=\"graf-image\" src=\"https:\/\/www.cybermedian.com\/cn\/wp-content\/uploads\/sites\/6\/2022\/02\/0xux3GjJiW2jYv65v.png\" data-image-id=\"0*xux3GjJiW2jYv65v.png\" data-width=\"532\" data-height=\"341\" \/><\/figure>\n<p id=\"c963\" class=\"graf graf--p graf-after--figure\"><a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/online.visual-paradigm.com\/app\/diagrams\/#diagram:proj=0&amp;type=VennDiagram&amp;gallery=\/repository\/1be9a579-7e80-40a2-97e0-9a307188b576.xml&amp;name=Mammals%20and%20Fish\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/online.visual-paradigm.com\/app\/diagrams\/#diagram:proj=0&amp;type=VennDiagram&amp;gallery=\/repository\/1be9a579-7e80-40a2-97e0-9a307188b576.xml&amp;name=Mammals%20and%20Fish\">\u7f16\u8f91\u6b64\u7ef4\u6069\u56fe<\/a><\/p>\n<h4 id=\"8a44\" class=\"graf graf--h4 graf-after--p\"><span id=\"Three_Circle_Venn_Diagram\">\u4e09\u5708\u7ef4\u6069\u56fe<\/span><\/h4>\n<p id=\"ace1\" class=\"graf graf--p graf-after--h4\">3 \u5708\u7ef4\u6069\u56fe\u662f\u4e00\u79cd\u5bf9\u5177\u6709\u76f8\u540c\u5c5e\u6027\u7684\u5bf9\u8c61\u7ec4\u8fdb\u884c\u5206\u7c7b\u7684\u65b9\u6cd5\u3002<\/p>\n<ul class=\"postList\">\n<li id=\"1fb3\" class=\"graf graf--li graf-after--p\">\u5b83\u6709\u4e09\u4e2a\u76f8\u4e92\u4ea4\u53c9\u7684\u5706\u5708\u3002<\/li>\n<li id=\"3aac\" class=\"graf graf--li graf-after--li\">\u6bcf\u4e2a\u5706\u90fd\u6709\u81ea\u5df1\u7684\u4e00\u7ec4\u8fdb\u5165\u5706\u7684\u4e8b\u7269\u7684\u5c5e\u6027\uff0c\u4f8b\u5982\u5947\u6570\u6216\u76f4\u89d2\u5f62\u72b6\u3002<\/li>\n<li id=\"3542\" class=\"graf graf--li graf-after--li\">\u5706\u5708\u4e4b\u5916\u8fd8\u6709\u4e00\u4e2a\u7a7a\u95f4\uff0c\u4e0d\u9002\u5408\u4efb\u4f55\u5c5e\u6027\u7684\u5bf9\u8c61\u53ef\u4ee5\u8fdb\u5165\u3002<\/li>\n<li id=\"82be\" class=\"graf graf--li graf-after--li\">\u4e0b\u56fe\u5411\u60a8\u5c55\u793a\u4e86\u5177\u6709 3 \u4e2a\u5706\u5708\u7684\u7ef4\u6069\u56fe\u662f\u5982\u4f55\u5de5\u4f5c\u7684\u3002<\/li>\n<\/ul>\n<figure id=\"0e54\" class=\"graf graf--figure graf-after--li\"><img decoding=\"async\" class=\"graf-image\" src=\"https:\/\/www.cybermedian.com\/cn\/wp-content\/uploads\/sites\/6\/2022\/02\/0Hinpjddxi9nMcTBx.png\" data-image-id=\"0*Hinpjddxi9nMcTBx.png\" data-width=\"648\" data-height=\"542\" \/><\/figure>\n<p id=\"0629\" class=\"graf graf--p graf-after--figure\">\u4ee5\u4e0b\u793a\u4f8b\u8bf4\u660e\u4e86\u4e0a\u8ff0\u96c6\u5408\u7684\u6982\u5ff5\u3002<\/p>\n<figure id=\"478a\" class=\"graf graf--figure graf-after--p\"><img decoding=\"async\" class=\"graf-image\" src=\"https:\/\/www.cybermedian.com\/cn\/wp-content\/uploads\/sites\/6\/2022\/02\/1-LkPJrT0hsihKziIBiL2xQ.png\" data-image-id=\"1*-LkPJrT0hsihKziIBiL2xQ.png\" data-width=\"413\" data-height=\"221\" \/><\/figure>\n<figure id=\"c510\" class=\"graf graf--figure graf-after--figure\"><img decoding=\"async\" class=\"graf-image\" src=\"https:\/\/www.cybermedian.com\/cn\/wp-content\/uploads\/sites\/6\/2022\/02\/0TCPe2E5ntB65pa_i.png\" data-image-id=\"0*TCPe2E5ntB65pa_i.png\" data-width=\"570\" data-height=\"553\" \/><\/figure>\n<p id=\"8f14\" class=\"graf graf--p graf-after--figure\"><a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/online.visual-paradigm.com\/app\/diagrams\/#diagram:proj=0&amp;type=VennDiagram&amp;gallery=\/repository\/a30110ac-719b-4cdd-906d-4ff26fcd2955.xml&amp;name=Gender%20vs%20Height%20vs%20Hobby\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/online.visual-paradigm.com\/app\/diagrams\/#diagram:proj=0&amp;type=VennDiagram&amp;gallery=\/repository\/a30110ac-719b-4cdd-906d-4ff26fcd2955.xml&amp;name=Gender%20vs%20Height%20vs%20Hobby\">\u7f16\u8f91\u6b64\u7ef4\u6069\u56fe<\/a><\/p>\n<h4 id=\"3a5a\" class=\"graf graf--h4 graf-after--p\"><span id=\"3_Circle_Venn_Diagram_Example_Aquatic_Creatures\">3 \u5706\u5f62\u7ef4\u6069\u56fe\u793a\u4f8b &#8211; \u6c34\u751f\u751f\u7269<\/span><\/h4>\n<p id=\"7ff0\" class=\"graf graf--p graf-after--h4\">\u901a\u8fc7\u6269\u5c55\u4e0a\u9762\u7684\u4f8b\u5b50\uff0c\u8fd9\u4e2a\u7ef4\u6069\u56fe\u7528\u6765\u663e\u793a\u6c34\u751f\u751f\u7269\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a\u9cb8\u9c7c\uff08\u54fa\u4e73\u52a8\u7269\uff09\u548c\u9c7c\u3001\u867e\uff08\u6c34\u751f\u751f\u7269\uff09\u3002\u5728\u5404\u4e2a\u9886\u57df\u90fd\u6709\u6c34\u751f\u751f\u7269\u7684\u7279\u70b9\u3002\u5728\u91cd\u53e0\u4e2d\uff0c\u751f\u7269\u5171\u4eab\u5c5e\u6027\uff1b\u5728\u91cd\u53e0\u4e4b\u5916\uff0c\u8fd9\u4e9b\u751f\u7269\u5177\u6709\u4e0d\u540c\u7684\u5c5e\u6027\u3002<\/p>\n<figure id=\"1703\" class=\"graf graf--figure graf-after--p\"><img decoding=\"async\" class=\"graf-image\" src=\"https:\/\/www.cybermedian.com\/cn\/wp-content\/uploads\/sites\/6\/2022\/02\/0g1xnSuJ8YMWJ8dHd.png\" data-image-id=\"0*g1xnSuJ8YMWJ8dHd.png\" data-width=\"521\" data-height=\"506\" \/><\/figure>\n<p id=\"1df0\" class=\"graf graf--p graf-after--figure\"><a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/online.visual-paradigm.com\/app\/diagrams\/#diagram:proj=0&amp;type=VennDiagram&amp;gallery=\/repository\/bbfef074-3d68-4585-8dd7-bf544f1177e2.xml&amp;name=Aquatic%20Creatures\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/online.visual-paradigm.com\/app\/diagrams\/#diagram:proj=0&amp;type=VennDiagram&amp;gallery=\/repository\/bbfef074-3d68-4585-8dd7-bf544f1177e2.xml&amp;name=Aquatic%20Creatures\">\u7f16\u8f91\u6b64\u7ef4\u6069\u56fe<\/a><\/p>\n<figure id=\"a594\" class=\"graf graf--figure graf-after--p\"><img decoding=\"async\" class=\"graf-image\" src=\"https:\/\/www.cybermedian.com\/cn\/wp-content\/uploads\/sites\/6\/2022\/02\/1QJ-Dgerqkw5WlrfAMTsQEw.png\" data-image-id=\"1*QJ-Dgerqkw5WlrfAMTsQEw.png\" data-width=\"525\" data-height=\"326\" \/><\/figure>\n<p id=\"572a\" class=\"graf graf--p graf-after--figure\"><a class=\"markup--anchor markup--p-anchor\" 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