Question

For any two setsA and B prove that

A intersection (A' union B ) = A intersection B

Answer 1

When three sets are A, B and C, then

A intersection (B union C​​​​​​) =(A intersection B​​​​​​) union(A intersection C​​​​​​)

(this is the distributive law of set)

So in this question

A intersection (A' union B​​​​​​) =(A intersection A'​​​​​​) union(A intersection B​​​​​​)

[ the union of any set and its it's complement is a null or zero set]

=0 union (A intersection B​​​​​​)
=(A intersection B​​​​​​)
[hence proved]