If A and B are two sets, then A B = A B iff - Vidyadip

MCQ

If $A$ and $B$ are two sets, then $A \cup B = A \cap B$ iff

A
$A \subseteq B$
B
$B \subseteq A$
✓
$A = B$
D
None of these

✓

Answer

Correct option: C.

$A = B$

c
(c) Let $x \in A \Rightarrow x \in A \cup B$,$[\because A \subseteq A \cup B]$

==> $x \in A \cap B$,$[\because A \cup B = A \cap B]$

==> $x \in A$ and $x \in B$ ==> $x \in B$, $\therefore A \subseteq B$

Similarly, $x \in B$ ==> $x \in A$, $\therefore B \subseteq A$

Now $A \subseteq B,\,\,B \subseteq A$ ==> $A = B$.

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