3章 集合の演算
GAIRON-book : 2018/6/21(19:23) 3.1. 和集合と積集合 35 定理3.5 集合A;B;Cに対して, 次が成り立つ. (1) AˆCかつBˆC)A[BˆC. (2) CˆAかつCˆB)CˆA\B. 証明 (1) a2A[Bとすると, a2Aまたはb2Bである. a2Aであれ ば, 仮定AˆCからa2Cである.また, a2Bであれば, 仮定BˆCから やはりa2Cである.いずれにせよ, a2CであるからA[BˆCが示された.
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