First slide

Operations on Sets

Question

If A, B, C are three sets such that $A \cap B = A \cap C a n d A \cup B = A \cup C$ , then

Moderate

A

B = C
B

$A \cap B = ϕ$
C

A = B
D

A = C

Solution

Let $x \in B \Rightarrow x \in A \cup B$
$\Rightarrow x \in A \cup C \Rightarrow x \in A o r x \in C$
If $x \in A, t h e n x \in A \cap B = A \cap C \Rightarrow x \in C$
So, $x \in B \Rightarrow x \in C$
Similarly $x \in B \Rightarrow x \in C,$ Hence B = C .

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