If A, B and C be the sets such that AUB = A U C and AnB = ANC, then B = C.
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prefer to it child
Step-by-step explanation:
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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