[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/116015#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/116015","headline":"\u5dee\u96c6\u5408 – Wikipedia","name":"\u5dee\u96c6\u5408 – Wikipedia","description":"\u3053\u306e\u8a18\u4e8b\u306f\u691c\u8a3c\u53ef\u80fd\u306a\u53c2\u8003\u6587\u732e\u3084\u51fa\u5178\u304c\u5168\u304f\u793a\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3001\u4e0d\u5341\u5206\u3067\u3059\u3002\u51fa\u5178\u3092\u8ffd\u52a0\u3057\u3066\u8a18\u4e8b\u306e\u4fe1\u983c\u6027\u5411\u4e0a\u306b\u3054\u5354\u529b\u304f\u3060\u3055\u3044\u3002\u51fa\u5178\u691c\u7d22?:\u00a0“\u5dee\u96c6\u5408”\u00a0\u2013\u00a0\u30cb\u30e5\u30fc\u30b9\u00a0\u00b7 \u66f8\u7c4d\u00a0\u00b7 \u30b9\u30ab\u30e9\u30fc\u00a0\u00b7 CiNii\u00a0\u00b7 J-STAGE\u00a0\u00b7 NDL\u00a0\u00b7 dlib.jp\u00a0\u00b7 \u30b8\u30e3\u30d1\u30f3\u30b5\u30fc\u30c1\u00a0\u00b7 TWL\uff082016\u5e742\u6708\uff09 \u5dee\u96c6\u5408\uff08\u3055\u3057\u3085\u3046\u3054\u3046\u3001\u82f1: set difference\uff09\u3068\u306f\u3001\u3042\u308b\u96c6\u5408\u306e\u4e2d\u304b\u3089\u5225\u306e\u96c6\u5408\u306b\u5c5e\u3059\u308b\u8981\u7d20\u3092\u53d6\u308a\u53bb\u3063\u3066\u5f97\u3089\u308c\u308b\u96c6\u5408\u306e\u3053\u3068\u3067\u3042\u308b[1]\u3002\u7279\u306b\u3001\u5168\u4f53\u96c6\u5408 U \u3092\u56fa\u5b9a\u3057\u3066\u3001U \u304b\u3089\u305d\u306e\u90e8\u5206\u96c6\u5408 A \u306e\u8981\u7d20\u3092\u53d6\u308a\u53bb\u3063\u3066\u5f97\u3089\u308c\u308b\u96c6\u5408\u3092 A \u306e\u88dc\u96c6\u5408\u3068\u3044\u3046[2]\u3002 \u5dee\u96c6\u5408","datePublished":"2022-03-18","dateModified":"2022-03-18","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/cd810e53c1408c38cc766bc14e7ce26a?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/cd810e53c1408c38cc766bc14e7ce26a?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/6\/64\/Question_book-4.svg\/50px-Question_book-4.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/6\/64\/Question_book-4.svg\/50px-Question_book-4.svg.png","height":"39","width":"50"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/116015","about":["wiki"],"wordCount":3913,"articleBody":"\u3053\u306e\u8a18\u4e8b\u306f\u691c\u8a3c\u53ef\u80fd\u306a\u53c2\u8003\u6587\u732e\u3084\u51fa\u5178\u304c\u5168\u304f\u793a\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3001\u4e0d\u5341\u5206\u3067\u3059\u3002\u51fa\u5178\u3092\u8ffd\u52a0\u3057\u3066\u8a18\u4e8b\u306e\u4fe1\u983c\u6027\u5411\u4e0a\u306b\u3054\u5354\u529b\u304f\u3060\u3055\u3044\u3002\u51fa\u5178\u691c\u7d22?:\u00a0“\u5dee\u96c6\u5408”\u00a0\u2013\u00a0\u30cb\u30e5\u30fc\u30b9\u00a0\u00b7 \u66f8\u7c4d\u00a0\u00b7 \u30b9\u30ab\u30e9\u30fc\u00a0\u00b7 CiNii\u00a0\u00b7 J-STAGE\u00a0\u00b7 NDL\u00a0\u00b7 dlib.jp\u00a0\u00b7 \u30b8\u30e3\u30d1\u30f3\u30b5\u30fc\u30c1\u00a0\u00b7 TWL\uff082016\u5e742\u6708\uff09\u5dee\u96c6\u5408\uff08\u3055\u3057\u3085\u3046\u3054\u3046\u3001\u82f1: set difference\uff09\u3068\u306f\u3001\u3042\u308b\u96c6\u5408\u306e\u4e2d\u304b\u3089\u5225\u306e\u96c6\u5408\u306b\u5c5e\u3059\u308b\u8981\u7d20\u3092\u53d6\u308a\u53bb\u3063\u3066\u5f97\u3089\u308c\u308b\u96c6\u5408\u306e\u3053\u3068\u3067\u3042\u308b[1]\u3002\u7279\u306b\u3001\u5168\u4f53\u96c6\u5408 U \u3092\u56fa\u5b9a\u3057\u3066\u3001U \u304b\u3089\u305d\u306e\u90e8\u5206\u96c6\u5408 A \u306e\u8981\u7d20\u3092\u53d6\u308a\u53bb\u3063\u3066\u5f97\u3089\u308c\u308b\u96c6\u5408\u3092 A \u306e\u88dc\u96c6\u5408\u3068\u3044\u3046[2]\u3002  \u5dee\u96c6\u5408 B \u2212 A \u306e\u30d9\u30f3\u56f3\u306b\u3088\u308b\u8996\u899a\u5316\uff08\u5de6\u304cA\u3001\u53f3\u304cB\u3002\uff09:B\u2216A\u00a0\u00a0=\u00a0\u00a0Ac\u2229B{displaystyle Bsetminus A~~=~~A^{c}cap B}  \u5dee\u96c6\u5408 A \u2212 B \u306e\u30d9\u30f3\u56f3\u306b\u3088\u308b\u8996\u899a\u5316\uff08\u5de6\u304cA\u3001\u53f3\u304cB\u3002\uff09:A\u2216B\u00a0\u00a0=\u00a0\u00a0A\u2229Bc{displaystyle Asetminus B~~=~~Acap B^{c}}\u96c6\u5408 B \u304b\u3089\u96c6\u5408 A \u306b\u5c5e\u3059\u308b\u5143\u3092\u9593\u5f15\u3044\u3066\u5f97\u3089\u308c\u308b\u96c6\u5408\u3092B\u2216A,B\u2216A{displaystyle Bsetminus A,quad Bsmallsetminus A}\u307e\u305f\u306f B \u2212 A \u3068\u8868\u73fe\u3057\u3001B \u304b\u3089 A \u3092\u5f15\u3044\u305f\u5dee\u3001\u5dee\u96c6\u5408\u3042\u308b\u3044\u306f B \u306b\u304a\u3051\u308b A \u306e\uff08\u76f8\u5bfe\uff09\u88dc\u96c6\u5408\u3068\u547c\u3076\u3002\u8a18\u53f7\u3092\u7528\u3044\u3066\u66f8\u3051\u3070\u3001x\u2208B\u2216A\u27fax\u2208B\u2227x\u2209A,{displaystyle xin Bsetminus Aiff xin Bland xnotin A,}\u3059\u306a\u308f\u3061B\u2216A={x\u2223x\u2208B\u2227x\u2209A}={x\u2208B\u2223x\u2209A}{displaystyle {begin{aligned}Bsetminus A&={xmid xin Bland xnotin A}\\&={xin Bmid xnotin A}end{aligned}}}\u304c\u5dee\u96c6\u5408\u306e\u5b9a\u7fa9\u3067\u3042\u308b\u3002\u3053\u308c\u306f A\u2282B{displaystyle Asubset B} \u3068\u306f\u9650\u3089\u306a\u3044\u5834\u5408\u306b\u3082\u5b9a\u7fa9\u3055\u308c\u308b\u3002\u5f8c\u8ff0\u306e\uff08\u7d76\u5bfe\uff09\u88dc\u96c6\u5408\u306e\u8a00\u8449\u3067\u66f8\u3051\u3070\u3001B\u2216A{displaystyle Bsetminus A} \u3068\u306f\u3001B \u306b\u304a\u3051\u308b A \u2229 B \u306e\u88dc\u96c6\u5408\u3067\u3042\u308b\u3002\u306a\u304a\u3001\u4e00\u822c\u306b\u96c6\u5408\u306e\u5dee\u306f\u4ea4\u63db\u6cd5\u5247\u3092\u6e80\u305f\u3055\u306a\u3044\uff1aA\u2216B\u2260B\u2216A.{displaystyle Asetminus Bneq Bsetminus A.}\u3053\u308c\u3089\u304c\u7b49\u3057\u304f\u306a\u308b\u306e\u306f\u3001A = B \u306e\u3068\u304d\u3001\u307e\u305f\u305d\u306e\u3068\u304d\u306b\u9650\u308b\u3002Table of Contents\u6ce8\u610f[\u7de8\u96c6]\u4f8b[\u7de8\u96c6]\u6ce8\u610f[\u7de8\u96c6]\u30c9\u30fb\u30e2\u30eb\u30ac\u30f3\u306e\u6cd5\u5247[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u6ce8\u610f[\u7de8\u96c6]\u96c6\u5408 A, B \u304c\u52a0\u6cd5 + \u3092\u6301\u3064\u4ee3\u6570\u7cfb\uff08\u7279\u306b\u52a0\u6cd5\u7fa4\uff09\u306e\u90e8\u5206\u96c6\u5408\u3067\u3042\u308b\u3068\u304d\u3001B \u2212 A \u306f\u96c6\u5408 {b \u2212 a | a \u2208 A, b \u2208 B} \u3068\u7d1b\u3089\u308f\u3057\u3044\u306e\u3067\u3053\u306e\u8a18\u6cd5\u3092\u4f7f\u7528\u3059\u308b\u306b\u306f\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3042\u308b\u3002\u4f8b[\u7de8\u96c6]  P = {1, 3, 5, 7, 9} (10 \u4ee5\u4e0b\u306e\u5947\u6570\u306e\u96c6\u5408)Q = {2, 3, 5, 7} (10 \u4ee5\u4e0b\u306e\u7d20\u6570\u306e\u96c6\u5408)\u3053\u306e\u3068\u304dP\u2216Q={1,9}{displaystyle Psmallsetminus Q={1,9}}\u3067\u3042\u308a\u3001  Q\u2216P={2}{displaystyle Qsmallsetminus P={2}}\u3067\u3042\u308b\u3002  \u88dc\u96c6\u5408\u306e\u30d9\u30f3\u56f3\u306b\u3088\u308b\u8996\u899a\u5316\uff08\u5de6\u304cA\u3001\u53f3\u304cB\u3002\uff09:Ac\u00a0\u00a0=\u00a0\u00a0\u2205c\u2216A{displaystyle A^{c}~~=~~emptyset ^{c}setminus A}\u5168\u4f53\u96c6\u5408\u3084\u666e\u904d\u96c6\u5408 (universe) \u306a\u3069\u3068\u547c\u3070\u308c\u308b\uff08\u5927\u304d\u306a\uff09\u96c6\u5408 U \u3092\u56fa\u5b9a\u3057\u3066\u3001\u305d\u306e\u90e8\u5206\u96c6\u5408\u306b\u3064\u3044\u3066\u306e\u307f\u8003\u3048\u3066\u3044\u308b\u3068\u304d\uff08\u4f8b\u3048\u3070\u3001U \u304c\u81ea\u7136\u6570\u5168\u4f53\u3001\u5b9f\u6570\u5168\u4f53\u3084\u3042\u308b\u4f4d\u76f8\u7a7a\u9593\u3067\u3042\u308b\u3068\u304d\u306a\u3069\uff09 U \u306e\u90e8\u5206\u96c6\u5408 A \u306b\u3064\u3044\u3066\u3001  U\u2216A{displaystyle Usmallsetminus A}\u3092 A \u306e\uff08\u7d76\u5bfe\uff09\u88dc\u96c6\u5408\uff08\u307b\u3057\u3085\u3046\u3054\u3046\u3001complement\uff09\u3068\u3044\u3044\u3001U\u304c\u4e86\u89e3\u3055\u308c\u3066\u3044\u308b\u6587\u8108\u3067\u306f\u5358\u306bAc,\u2201A,A\u00af{displaystyle A^{mathrm {c} },,complement A,,{overline {A}}}\u306a\u3069\u3068\u8868\u3059\u3002\u3042\u308b\u96c6\u5408\u306e\u88dc\u96c6\u5408\u306e\u88dc\u96c6\u5408\u306f\u3082\u3068\u306e\u96c6\u5408\u81ea\u8eab\u3067\u3042\u308b\u3002\u81ea\u7136\u6570\u306b\u3064\u3044\u3066\u8003\u3048\u3066\u3044\u308b\u3068\u304d\u3001\u5947\u6570\u5168\u4f53\u306e\u96c6\u5408\u306e\u88dc\u96c6\u5408\u306f\u5076\u6570\u5168\u4f53\u306e\u96c6\u5408\u3067\u3042\u308b\u3002\u5b9f\u6570\u5168\u4f53 R \u306b\u3064\u3044\u3066\u8003\u3048\u3066\u3044\u308b\u3068\u304d\u3001\u6709\u7406\u6570\u5168\u4f53 Q \u306e\u88dc\u96c6\u5408 R\u2216Q{displaystyle mathbf {R} setminus mathbf {Q} } \u306f\u7121\u7406\u6570\u5168\u4f53\u3067\u3042\u308b\u3002\u6ce8\u610f[\u7de8\u96c6]P \u306e\u88dc\u96c6\u5408\u3092 Pc \u3068\u8868\u3059\u5834\u5408\u3001\u304a\u304a\u304f\u306f P \u304c P \u306e\u9589\u5305 \u3092\u3042\u3089\u308f\u3059\u3002\u9006\u306b P \u304c\u88dc\u96c6\u5408\u3092\u8868\u3057\u3066\u3044\u308b\u3088\u3046\u306a\u6587\u8108\u3067\u306f\u3001Pc \u3067 P \u306e\u9589\u5305 (closure) \u3092\u8a18\u3059\u3053\u3068\u304c\u3042\u308b\u3002\u30c9\u30fb\u30e2\u30eb\u30ac\u30f3\u306e\u6cd5\u5247[\u7de8\u96c6]P, Q \u3092\u3042\u308b\u96c6\u5408\u306e\u90e8\u5206\u96c6\u5408\u3068\u3059\u308b\u3068\u304d\u3001(P\u222aQ)c=Pc\u2229Qc(P\u2229Q)c=Pc\u222aQc{displaystyle {begin{aligned}(Pcup Q)^{mathrm {c} }&=P^{mathrm {c} }cap Q^{mathrm {c} }\\(Pcap Q)^{mathrm {c} }&=P^{mathrm {c} }cup Q^{mathrm {c} }end{aligned}}}\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u304c\u5206\u304b\u308b[3]\u3002\u3053\u308c\u306f\u3082\u3063\u3068\u4e00\u822c\u5316\u3067\u304d\u3066\u3001{P\u03bb}\u03bb\u2208\u039b \u3092\u3042\u308b\u57fa\u790e\u3068\u306a\u308b\u96c6\u5408\u306e\u90e8\u5206\u96c6\u5408\u306e\u65cf\u3068\u3059\u308b\u3068\u304d\u306b\u3001(\u22c3\u03bb\u2208\u039bP\u03bb)c=\u22c2\u03bb\u2208\u039bP\u03bbc(\u22c2\u03bb\u2208\u039bP\u03bb)c=\u22c3\u03bb\u2208\u039bP\u03bbc{displaystyle {begin{aligned}left(bigcup _{lambda in Lambda }P_{lambda }right)^{mathrm {c} }&=bigcap _{lambda in Lambda }P_{lambda }^{mathrm {c} }\\left(bigcap _{lambda in Lambda }P_{lambda }right)^{mathrm {c} }&=bigcup _{lambda in Lambda }P_{lambda }^{mathrm {c} }end{aligned}}}\u304c\u6210\u308a\u7acb\u3064\u3002\u3053\u308c\u3089\u3092\u30c9\u30fb\u30e2\u30eb\u30ac\u30f3\u306e\u6cd5\u5247\u3068\u3044\u3046\u3002\u3053\u306e\u6cd5\u5247\u306f\u3001\u5bfe\u5fdc\u3059\u308b\u8ad6\u7406\u8a18\u53f7\u306e\u6027\u8cea\uff08\u7279\u306b\u53cc\u5bfe\u6027\uff09\u3092\u53cd\u6620\u3057\u305f\u3082\u306e\u3067\u3042\u308b\u3002\u8a73\u3057\u304f\u306f\u8a18\u53f7\u8ad6\u7406\u5b66\u306e\u9805\u76ee\u3092\u53c2\u7167\u3002\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/116015#breadcrumbitem","name":"\u5dee\u96c6\u5408 – Wikipedia"}}]}]