Prove the distributive laws for sets a A n B U C A n B U A

Prove the \" distributive laws\" for sets:

a) A n (B U C) = (A n B) U (A n C)

b) A U ( B n C) = ( A U B) n (A U C).

Solution

One proof that A ? (B ? C) = (A ? B) ? (A ? C) is to follow the same strategy as in (a) by showing the two required containments. Another proof that A ? (B ? C) = (A ? B) ? (A ? C) can be given using de Morgan