Let X and Y be two sets.Statement 1:X∩(Y∪X)′=ϕStatement 2: If X∪ Y has m elements and X∩ Y has n elements then symmetric difference X ∆ Y has m – n elements.

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STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is False

STATEMENT-1 is False, STATEMENT-2 is True

answer is B.

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Detailed Solution

X∩(Y∪X)′=X∩Y′∩X′=X∩X′∩Y′=ϕStatement-1 is True.XΔY=(X~Y)∪(Y~X)=(X∪Y)~(X∩Y)⇒number of elements in X ∆Y = m – n. ⇒ Statement-2 is True but does explain statement-1.

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