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Question

Let P and Q be two sets then what is (PQ)(PQ) equal to ?

A
(PQ)(PQ)=ξQ=ξQ=ξ
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B
(PQ)(PQ)=ξQ=ξQ=ξ
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C
(PQ)(PQ)=ξQ=ξQ=ξ
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D
none of the above
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Solution

The correct option is B (PQ)(PQ)=ξQ=ξQ=ξ
(PQ)(PQ)=(PQ)(PQ)
=(PP)(PQ)(QP)(QQ)
=ξ{Q(PP)}Q
=ξ{Qξ)Q
=ξQQ=ξQ=ξ

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