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If A, B and C are three sets such that A∩B = A∩C and A∪B = A∪C, then

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If A, B and C are three sets such that A∩B = A∩C and A∪B = A∪C, then

(A)  A = B

(B)  A = C

(C)  B = C

(D)  A∩B  = φ

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1 Answer

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Best answer

Correct option (C) B = C

Explanation :

A∪B = A∪C

⇒ (A∪B)∩C =(A∪C)∩C

⇒ (A∩C)∪(B∩C) = C    ....(i)

Again,

A∪B = A∪C

⇒ (A∪B)∩C =(A∪C)∩C

⇒ B = (A∩B) ∪ (B ∩ C)

From Eqs. (1) and (2),

B = C

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