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 and x ϵ C}
= {5, 6}
A ∪ (B ∩ C) = {x: x ϵ A or x ϵ (B ∩ C) }
= {1, 2, 4, 5, 6}.
R.H.S =
(A ∪ B) = {x: x ϵ A or x ϵ B }
= {1, 2, 4, 5, 6}.
(A ∪ C) = {x: x ϵ A or x ϵ C }
= {1, 2, 4, 5, 6, 7}.
(A ∪ B) ∩ (A ∪ C) = {x:x ϵ (A ∪ B) and x ϵ (A ∪ C) }.
= {1, 2, 4, 5, 6}.
Hence Verified.