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Question

If X and Y are two sets and X denotes the complement of X, then X(XY) = ___.

A
X
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B
Y
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C
ϕ
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D
XY
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Solution

The correct option is C ϕ
X(XY)=X(XY) [(AB)=AB]=(XX)Y [A(BC)=(AB)C]=ϕY [AA=ϕ]=ϕ [ϕA=ϕ]

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