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Question

If A, B and C are three sets such that AB=AC and AB=AC, then


A

A=C

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B

B=C

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C

AB=ϕ

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D

A=B

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Solution

The correct option is B

B=C


Given that AB=AC and AB=AC
(AB)C=(AC)C
(AC)(BC)=C [(AC)C=C]
(AB)(BC)=C......(1)

Again AB=AC
(AB)B=(AC)B
B=(AB)(CB)
=(AB)(BC)......(2)

From (1) and (2) we get,
B=C


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