2018骞存垚浜洪珮鑰冨皥鍗囨湰鏁�(sh霉)瀛搁泦鍚堝拰绨℃槗閭忚集涓�


鐩搁棞(gu膩n)鎺ㄨ枽锛�2018骞存垚鑰冭€冨墠鍚勭寰╃繏娌栧埡瑷堝妰
2018骞存垚浜洪珮鑰冨皥鍗囨湰鏁�(sh霉)瀛搁泦鍚堝拰绨℃槗閭忚集涓�
銆愰泦鍚堣垏闆嗗悎鐨勯棞(gu膩n)绯汇€�
涓€浜涚郸瀹氱殑闆嗗悎锛屽畠鍊戜箣闁撳彲浠ユ湁绋ó闂�(gu膩n)绯伙紝涓嶉亷锛屾渶鍩烘湪鐨勮绠�“鍖呭惈”鑸�“鐩哥瓑”鐨勯棞(gu膩n)绯�銆�
1.瀛愰泦锛氬皪浜庡叐鍊嬮泦鍚圓鍜孊,濡傛灉闆嗗悎A鐨勪换浣曚竴鍊嬪厓绱犻兘鏄泦鍚圔鐨勫厓绱�锛屽墖闆嗗悎A 鍙仛闆嗗悎B鐨勫瓙闆�锛岃浣淎⊆B 鎴� B⊇A锛�
璁€浣�“A鍖呭惈浜嶣”锛屾垨“B鍖呭惈A”.
瀛愰泦鐨勬€ц唱(zh矛)锛�
(1) 浠讳綍涓€鍊嬮泦鍚圓鏄畠鏈韩鐨勫瓙闆嗭細A⊆A,鍥犵偤闆嗗悎A鐨勪换浣曚竴鍊嬪厓绱犻兘灞簬闆嗗悎A鏈韩;
(2) 绌洪泦鏄换浣曚竴鍊嬮泦鍚圓鐨勫瓙闆嗭細肖∊A;
(3) 灏嶄簬闆嗗悎 A銆丅銆丆, 濡� A⊆B, B⊆C,鍓� A⊆C.
2. 闆嗗悎鐩哥瓑锛氬皪浜庡叐鍊嬮泦鍚圓鑸嘊,濡傛灉A⊆B,鍚屾檪B⊆A,閭d箞绋遍泦鍚圓鑸囬泦鍚圔鐩哥瓑锛岃浣淎 = B,
璁€浣滐細“A绛変簬B”閫欏氨鏄锛岄泦鍚圓鐨勪换浣曚竴鍊嬪厓绱犻兘鏄泦鍚圔鐨勫厓绱�;鍙嶄箣锛岄泦鍚圔鐨勪换浣� 涓€鍊嬪厓绱犻兘鏄泦鍚圓鐨勫厓绱�.鍥犺€岄€欏叐鍊嬮泦鍚堝寘鍚殑鍏冪礌瀹屽叏涓€妯�锛屽叐鍊嬮泦鍚堟槸鍚屼竴鍊嬮泦鍚�.
3. 鐪熷瓙闆嗭細濡傛灉涓擜⊆B涓擜≠B鍓囩ū闆嗗悎A鐐洪泦鍚圔鐨勭湡瀛愰泦锛岃浣�
A⊊B鎴� B⊋A,
閫氬父琛ㄧず鐐� A⊂B鎴朆⊃A.
涓嬮潰鏄父瑕嬪咕绋暩(sh霉)闆嗙殑闂�(gu膩n)绯伙細
N⊊Z, Z⊊Q, Q⊊R.
4. 浜ら泦锛氱敱鎵€鏈夋棦灞簬闆嗗悎A鍙堝爆浜庨泦鍚圔鐨勫厓绱犳墍绲勬垚鐨勯泦鍚�锛屽彨鍋氶泦鍚圓鑸囬泦鍚圔鐨勪氦闆�锛岃浣淎∩B.璁€浣�“A浜(鍦�1.2)锛屽嵆
A∩B= {x | x∈A 涓攛∈B}
鍦�1. 2 鍦�1. 3
浜ら泦鐨勬€ц唱(zh矛)锛�
(1) A∩A = A; (2) A∩肖=肖; (3) A∩B=B∩A (浜ゆ彌寰�).
5. 骞堕泦锛氱敱鎵€鏈夊爆浜庨泦鍚圓鎴�?q奴)鍎嗚顕灖鐨勫厓绱犳墍绲勬垚鐨勯泦鍚堬紝鍙仛闆嗗悎A鑸囬泦鍚圔鐨勫苟闆�锛岃浣淎UB锛岃畝浣�“A骞禕”(濡傚湒1.3),鍗�
A⋃B= {x /X∊A 鎴杧∊B}.骞堕泦鐨勬€ц唱(zh矛)锛�
(1) AUA=A; (2) AU肖=A, (3) AUB = BUA (浜ゆ彌寰�).
6. 鍏ㄩ泦鑸囪闆�
(1)鍏ㄩ泦锛氬湪鐮旂┒鏌愪簺闆嗗悎鑸囬泦鍚堜箣闁撶殑闂�(gu膩n)绯绘檪锛屽鏋滈€欎簺闆嗗悎閮芥槸鏌愪竴鍊嬮泦鍚堢殑瀛愰泦锛屽墖閫欏€嬬郸瀹氱殑闆嗗悎鍙仛鍏ㄩ泦锛岀敤绗﹁櫉U琛ㄧず.閫欏氨鏄锛屽叏闆嗗惈鏈夋墍瑕佺爺绌剁殑鍚勫€嬮泦鍚堢殑鍏ㄩ儴鍏冪礌銆�
渚嬪锛屽湪鐮旂┒鏁�(sh霉)闆嗘檪锛屽父甯告妸瀵︽暩(sh霉)闆哛浣滅偤鍏ㄩ泦;鍦ㄧ爺绌跺湒褰㈢殑闆嗗悎鏅傦紝甯稿父鎶婃墍鏈夌殑绌洪枔鍦栧舰绲勬垚鐨勯泦鍚堜綔鐐哄叏闆�.
娉ㄦ剰锛氬叏闆嗘槸鐩稿皪浜庢墍瑷庤珫鐨勫晱椤岃€岃█鐨�锛屼竴鍊嬮泦鍚堝湪涓€瀹氭浠朵笅鏄叏闆�锛屽湪鍙︿竴鍊嬫浠朵笅灏卞彲鑳戒笉鏄叏闆�.渚嬪锛岃◣璜栫殑闆嗗悎鍍呭惈鏁存暩(sh霉)鍏冩檪锛屽墖鏁存暩(sh霉)闆嗗彲浣滅偤鍏ㄩ泦;鑻ヨ◣璜栫殑闆嗗悎鍖呮嫭鍒嗘暩(sh霉)鍏冩檪锛屽墖鏁存暩(sh霉)闆嗕笉鏄叏闆�锛岃€屾湁鐞嗘暩(sh霉)闆嗘垨?q奴)宕�?sh霉)闆嗗墖鍙綔鐐哄叏闆�.
(2)瑁滈泦锛氬鏋滃凡鐭ュ叏闆嗙偤U锛屼笖闆嗗悎A⊆U锛屽墖鐢盪涓墍鏈変笉灞簬A鐨勫厓绱犵祫鎴愮殑闆嗗悎锛屽彨鍋歎涓瓙闆咥鐨勮闆嗭紝瑷樹綔CuA锛岀暥鏄庣⒑鏅�锛岀啊瑷樹綔CA (璁€浣�“A瑁�”)锛屽嵆
CA= {x |x∊U 涓� x∉A
鍦�1.4 涓殑闀锋柟褰㈠収(n猫i)琛ㄧず鍏ㄩ泦U锛屽湏鐨勫収(n猫i)閮ㄨ〃绀洪泦鍚圓,鏂滅窔閮ㄥ垎琛ㄧず闆嗗悎A鍦ㄩ泦鍚圲涓殑 瑁滈泦CA.鎻涘彞瑭辫锛岄泦鍚圓鐨勮闆咰A鏄緸鍏ㄩ泦U涓櫎鍘婚泦鍚圓鐨勫厓绱犲悗鍓╀笅鐨勫厓绱犵祫鎴愮殑闆嗗悎.濡俇=R= {瀵︽暩(sh霉)}锛孮= {鏈夌悊鏁�(sh霉)}锛屽墖Q鐨勮闆嗙偤 CQ= {鐒$悊鏁�(sh霉)}.
鍏ㄩ珨鐒$悊鏁�(sh霉)鐨勯泦鍚圕Q鍙仛鐒$悊鏁�(sh霉)闆�
鍦�1.4
鏈€鏂拌硣瑷�
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