Q. 2 C4.7( 3 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 is defined as {x ϵ B : x C}

B = {2, 3, 5, 6}

C = {4, 5, 6, 7}

B–C = {2, 3}

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

= {2}

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) is defined as {x ϵ (A B) : x (A C)}

= {2}.

Hence Verified.

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RS Aggarwal - Mathematics