集合定律 逻辑定律 Let X denote a set,and A,B,and C denote subsets of X.Then (DeMorgan's laws) (PVQ)4(一PAQ): 1.0≤A and A≤A. -(PAQ)+(PV=Q)月 2.(A°=A. (Distributive property)(PA(QVR))((PAQ)v(PAR)): 3.AU0=A. (PV(QAR)((PVQ)A(PVR)): 4.A∩0=0. (Double negation) (一P)4P: 5.A∩A=A. 6.AUA=A. 7.AnB=BnA.(Commutative property) (Associative property) (PA(QAR))((PAQ)AR) 8.AUB=BUA.(Commutative property) (PV(QVR))((PVQ)VR); 9.(AUB)UC=AU(BUC).(Associative property) 10.(A∩B)∩C=A∩(BnC).(Associative property) (Commutative property) (PAQ)分(QAP): 11.A∩B≤A. (PVQ)+(Q V P). 12.A∈AUB. 13.AU(BnC)=(AUB)(AUC).(Distributive property) 14.An(BUC)=(AnB)U(AnC).(Distributive property) 15.X(AUB)=(XA)n(X\B).(DeMorgan's law) (When X is the universe we also write (AUB)=Acn Be.) 16.X(AnB)=(XA)U(X\B).(DeMorgan's law) (When X is the universe we also write (AnB)=AcU Be.) 17.A\B=A∩B.集合定律 逻辑定律