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.