Question

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

• A. $A\subseteq B$
• B. $B\subseteq A$
• C. $A=B$
• D. None of these

Answer 1

Answer: (C)

$A=B$

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

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

$\Rightarrow x\in A$ and $x\in B,\therefore A\subseteq B$

Similarly, $x\in B\Rightarrow x\in A,B\subseteq A$

Now $A\subseteq B$, $B\subseteq A$ $\Rightarrow A=B$