Answer :
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.
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