Q2 of 162 Page 1

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).

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


Now,


B ∪ C = {5, 6}


A ∩ (B ∪ C) = {5}


Similarly finding out R.H.S we get,


A ∩ B = {2, 5}


A ∩ C = {4, 5}


(A ∩ B) ∩ (A ∩ C) = {5}


L.H.S = R.H.S


Hence, Verified.


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2

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)

 2

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)

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(A ∪ B)’ = A’ ∩ B’

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If U = {2, 3, 5, 7, 9} is the universal set and A = {3, 7}, B = {2, 5, 7, 9}, then prove that: