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

The correct option is C

$A=B$

Explanation for the correct option:

Finding the value:

Let $x\in A$

$\Rightarrow x\in A\cup B$ $\left[\mathbf{\because }\mathit{A}\mathbf{}\mathbf{\subseteq }\mathbf{}\mathit{A}\mathbf{}\mathbf{\cup }\mathbf{}\mathit{B}\right]$

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

$\Rightarrow x\in A$and $x\in B$

$\therefore A\subseteq B$

Similarly, $x\in B$

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

Now, $A\subseteq B,B\subseteq A$

$\Rightarrow A=B$

Hence, Option ‘C’ is Correct.