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)

Question

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)

Philoid · Accepted Answer

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.

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)