Question

If A = {a, b, c, d, e}, B = {a, c, e, g} and C = {b, e, f, g}, find (i) A∩ (B-C) (ii) A-(BU C) (iii) A - (B∩ C)

Answer 1

Given that AUB = AUC

⇒ (AUB) ∩ C = (AUC) ∩C

⇒ (A∩C) U (B∩C) = C [ ∴(AUC)∩C = C ]

⇒ (A∩B) U (B∩C) = C ..........(1) [ ∴(A∩C) = A∩B ]

Again AUB = AUC

(AUB) ∩ B = (AUC) ∩ B

B = (A∩B) U (C∩B)

= (A∩B) U (B∩C) ...........(2)

From 1 & 2 we get

B = C

I hope you are understand my solution