First slide

Operations on Sets

Question

If $A \cap B = B$ , then

Easy

A

$A \subseteq B$
B

$B \subseteq A$
C

$A = B$
D

None of these

Solution

Let $x \in A \Rightarrow x \in A \cup B, [∵ A \subseteq A \cup B]$
$\Rightarrow x \in A \cap B, [∵ A \cup B = A \cap B]$
$\Rightarrow x \in A and x \in B \Rightarrow x \in B, ∴ A \subseteq B$
Similarly, $x \in B \Rightarrow x \in A, ∴ B \subseteq A$
Now $A \subseteq B, B \subseteq A \Rightarrow A = B$ .

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