基本证明方式(3) ■利用已知恒等式或等式作集合代数推演 1.0C A and A CA. 13.AU(BnC)=(AUB)(AUC).(Distributive property) 2.(Ac)=A. 14.An(BUC)=(AnB)U(AnC).(Distributive property) 3.AU0=A. 15.X(AUB)=(XA)(X B).(DeMorgan's law) 4.An0=0. (When X is the universe we also write (AUB)c=AnB. 5.AnA=A. 16.X(AnB)=(XA)(XB).(DeMorgan's law) 6.AUA=A. (When X is the universe we also write (AnB)c=AcUBe. 7.AnB=BA.(Commutative property) 17.A\B=AOBC. 8.AUB=BUA.(Commutative property) 18.A CB if and only if (X B)C(XA). 9.(AUB)UC=AU(BUC).(Associative property) (When X is the universe we also write A C B if and only if BeCAc.) 10.(AnB)nC=An(BC).(Associative property) 19.A CC and BC C if and only if AUBCC. 11.AnBCA. 20.CCA and CC B if and only ifC CAnB. 12.ACAUB. 21.AUB=A if and only if BCA. 22.AnB=B if and only if B C A.基本证明方式（3） ◼ 利用已知恒等式或等式作集合代数推演