Question

(A ∩ B) ∪ (A ∩ B‘) = A

Answer 1

let A={1,2,3,4}
B={2,3,4,6,7,8}
U={1,2,3,4,5,6,7,8,9}
LHS,
AΠB={2,3,4}
B'= U-B
= {1,5,9}
AΠB'={1}
; (AΠB) U (AΠB')={1,2,3,4}
Therefore,
(AΠB) U (AΠB') = A
Hence, proved