Rozwiązane

Należy wykazać (dowieść) słuszność twierdzeń:
(AnB)uB=B
(A\B)nC=(AnC)\B
(AxB)n(CxD)=(AnC)x(BnD)
A\B\C=A\C\B=A\(BuC)

Odpowiedź :

Cyfraviz
o - zbiór pusty

(A n B) u B = B
L = (A n B) u B = (A u B) n (B u B) = (A\B u B) n B = (A\B n B) u (B n B) = o u B = B = P

(A\B) n C = (A n C)\B
L = (A\B) n C = (A n B') n C = A n B' n C = A n C n B' = (A n C) n B' = (A n C)\B = P

(AxB)n(CxD) = (AnC)x(BnD)

A\B\C = A\C\B = A\(B u C)
L = A\B\C = (A\B)\C = (A n B')\C = (A n B') n C' = A n B' n C' = A n C' n B' = (A n C') n B' = (A\C)\B = A\C\B = S = A\C\B = (A\C)\B = (A n C') n B' = A n C' n B' = A n (C' n B') = A n (C n B)' = A\(C n B) = P

Viz Inne Pytanie