First slide

Operations on Sets

Question

If $X$ and $Y$ are two sets such that $X \cap Y = X \cup Y,$ then

Moderate

A

$X \subset Y, X \neq Y$
B

$Y \subset X, Y \neq X$
C

$X = Y$
D

none of these

Solution

$X \subset Y \Rightarrow X \cap Y = X, X \cup Y = Y$
$Y \subset X \Rightarrow X \cap Y = Y, X \cup Y = X .$
So, $X \cap Y = X \cup Y \Rightarrow X = Y$

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