Question

prove that
A n (B∆C) = (AnB)
∆(AnC)​

Answer 1

Answer:

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