Q. 2 E5.0( 2 Votes )

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)

(B C) = {x:x ϵ B and x ϵ C}

= {5, 6}

(A – (B C)) =

A–(B C) is defined as {x ϵ A : x (B C)}

A = {1, 2, 4, 5}

(B C) = {5, 6}

(A – (B C)) = {1, 2, 4}

R.H.S:

(A – B) =

A–B is defined as {x ϵ A : x B}

A = {1, 2, 4, 5}

B = {2, 3, 5, 6}

A–B = {1, 4}

(A–C) =

A–C is defined as {x ϵ A : x C}

A = {1, 2, 4, 5}

C = {4, 5, 6, 7}

A–C = {1, 2}

(A – B) (A–C) = {x:x ϵ (A – B) OR x ϵ (A – C) }.

= {1, 2, 4}

Hence verified.

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RS Aggarwal - Mathematics