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Simplify X∩(X∪Y)' to the Empty Set | JEE Sets

JEE Maths question with a full step-by-step solution.

Question
If XX and YY are two sets and XX' denotes the complement of XX, then X(XY)X \cap (X \cup Y)' is equal to:
AXX
BYY
Cϕ\phicorrect
DXYX \cap Y
Solution
By De Morgan's law, (XY)=XY(X \cup Y)' = X' \cap Y'. Hence
X(XY)=X(XY)=(XX)Y=ϕY=ϕ.X \cap (X \cup Y)' = X \cap (X' \cap Y') = (X \cap X') \cap Y' = \phi \cap Y' = \phi.
Correct answer: (3)
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