Question

if A, B and C be the sets such that A union B =A union C and A intersection B =A intersection C then prove that B =C.​

Answer 1

Answer:

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Answer 2

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

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