Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identities:
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
L.H.S.
(B ∪ C) = {x: x ϵ B or x ϵ C }
= {2, 3, 4, 5, 6, 7}.
(A ∩ (B ∪ C)) = {x:x ϵ A and x ϵ (B ∪ C)}
= {2, 4, 5}
R.H.S:
(A ∩ B) = {x:x ϵ A and x ϵ B}
= {2, 5}
(A ∩ C) = {x:x ϵ A and x ϵ C}
= {4, 5}
(A ∩ B) ∪ (A ∩ C) = {x:x ϵ (A∩B) and x ϵ (A∩C) }.
= {2, 4, 5}.
Hence verified.