2018骞存垚浜洪珮鑰冨皥(zhu膩n)鍗囨湰鏁�(sh霉)瀛�(xu茅)闆嗗悎鍜岀啊(ji菐n)鏄撻倧杓笁


鐩搁棞(gu膩n)鎺ㄨ枽锛�2018骞存垚鑰冭€冨墠鍚勭寰�(f霉)缈�(x铆)娌栧埡瑷�(j矛)鍔�
2018骞存垚浜洪珮鑰冨皥(zhu膩n)鍗囨湰鏁�(sh霉)瀛�(xu茅)闆嗗悎鍜岀啊(ji菐n)鏄撻倧杓笁
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�锛屼笉閬�(gu貌)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(du矛)浜庡叐鍊�(g猫)闆嗗悎A鍜孊,濡傛灉闆嗗悎A鐨勪换浣曚竴鍊�(g猫)鍏冪礌閮芥槸闆嗗悎B鐨勫厓绱�锛屽墖闆嗗悎A 鍙仛闆嗗悎B鐨勫瓙闆嗭紝瑷樹綔A⊆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�(g猫)闆嗗悎A鏄畠鏈韩鐨勫瓙闆嗭細A⊆A,鍥�?y脿n)姒ь嚡铻︾殑浠讳綍涓€鍊�(g猫)鍏冪礌閮藉爆浜庨泦鍚圓鏈韩;
(2) 绌洪泦鏄换浣曚竴鍊�(g猫)闆嗗悎A鐨勫瓙闆嗭細肖∊A;
(3) 灏�(du矛)浜庨泦鍚� A銆丅銆丆, 濡� A⊆B, B⊆C,鍓� A⊆C.
2. 闆嗗悎鐩哥瓑锛氬皪(du矛)浜庡叐鍊�(g猫)闆嗗悎A鑸嘊,濡傛灉A⊆B,鍚屾檪(sh铆)B⊆A,閭d箞绋�(ch膿ng)闆嗗悎A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(shu艒)锛岄泦鍚圓鐨勪换浣曚竴鍊�(g猫)鍏冪礌閮芥槸闆嗗悎B鐨勫厓绱�;鍙嶄箣锛岄泦鍚圔鐨勪换浣� 涓€鍊�(g猫)鍏冪礌閮芥槸闆嗗悎A鐨勫厓绱�.鍥犺€岄€欏叐鍊�(g猫)闆嗗悎鍖呭惈鐨勫厓绱犲畬鍏ㄤ竴妯�锛屽叐鍊�(g猫)闆嗗悎鏄悓涓€鍊�(g猫)闆嗗悎.
3. 鐪熷瓙闆嗭細濡傛灉涓擜⊆B涓擜≠B鍓囩ū(ch膿ng)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�(ji脿n)骞剧ó鏁�(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堬紝鍙仛闆嗗悎A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�锛屽彨鍋氶泦鍚圓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(b菙)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(sh铆)锛屽鏋滈€欎簺闆嗗悎閮芥槸鏌愪竴鍊�(g猫)闆嗗悎鐨勫瓙闆�锛屽墖閫欏€�(g猫)绲﹀畾鐨勯泦鍚堝彨鍋氬叏闆嗭紝鐢ㄧ铏�(h脿o)U琛ㄧず.閫欏氨鏄(shu艒)锛屽叏闆嗗惈鏈夋墍瑕佺爺绌剁殑鍚勫€�(g猫)闆嗗悎鐨勫叏閮ㄥ厓绱犮€�
渚嬪锛屽湪鐮旂┒鏁�(sh霉)闆嗘檪(sh铆)锛屽父甯告妸瀵�(sh铆)鏁�(sh霉)闆哛浣滅偤鍏ㄩ泦;鍦ㄧ爺绌跺湒褰㈢殑闆嗗悎鏅�(sh铆)锛屽父甯告妸鎵€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(du矛)浜庢墍瑷庤珫鐨勫晱(w猫n)椤岃€岃█鐨�锛屼竴鍊�(g猫)闆嗗悎鍦ㄤ竴瀹氭浠朵笅鏄叏闆�锛屽湪鍙︿竴鍊�(g猫)姊濅欢涓嬪氨鍙兘涓嶆槸鍏ㄩ泦.渚嬪锛岃◣璜栫殑闆嗗悎鍍呭惈鏁存暩(sh霉)鍏冩檪(sh铆)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�?j菒n)?sh霉)鍏冩檪(sh铆)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�(b菙)闆嗭細濡傛灉宸茬煡鍏ㄩ泦鐐篣锛屼笖闆嗗悎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(b菙)闆�锛岃浣淐uA锛岀暥(d膩ng)鏄庣⒑鏅�(sh铆)锛岀啊(ji菐n)瑷樹綔CA (璁€浣�“A瑁�(b菙)”)锛屽嵆
CA= {x |x∊U 涓� x∉A
鍦�1.4 涓殑闀�(zh菐ng)鏂瑰舰鍏�(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�(b菙)闆咰A.鎻涘彞瑭辫(shu艒)锛岄泦鍚圓鐨勮(b菙)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�(sh铆)鏁�(sh霉)}锛孮= {鏈夌悊鏁�(sh霉)}锛屽墖Q鐨勮(b菙)闆嗙偤 CQ= {鐒�(w煤)鐞嗘暩(sh霉)}.
鍏ㄩ珨鐒�(w煤)鐞嗘暩(sh霉)鐨勯泦鍚圕Q鍙仛鐒�(w煤)鐞嗘暩(sh霉)闆�
鍦�1.4
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