Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the identities A ∩ (B △ C) = (A ∩ B) △ (A ∩ C)

Asked by Aaryan | 2 years ago |  93

1 Answer

Solution :-

A ∩ (B △ C) = (A ∩ B) △ (A ∩ C)

A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}.

Firstly let us consider the LHS

A ∩ (B △ C)

B △ C = (B – C) ∪ (C – B) = {2, 3} ∪ {4, 7} = {2, 3, 4, 7}

A ∩ (B △ C) = {2, 4}

Now, RHS

A ∩ B = {2, 5}

A ∩ C = {4, 5}

(A ∩ B) △ (A ∩ C) = [(A ∩ B) – (A ∩ C)] ∪ [(A ∩ C) – (A ∩ B)]

= {2} ∪ {4}

= {2, 4}

∴ LHS = RHS

Hence, Verified.

Answered by Sakshi | 2 years ago

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