Question

For two sets A and B, $A\cup B=A$ if and only if

• A. $B\subseteq A$
• B. $A\subseteq B$
• C. $B\ne A$
• D. $A\cap B=\varphi$

Answer 1

The correct option is A $B\subseteq A$

$A\cup B$ gives the the elements that are either in set $A$ or in set $B$.

$\Rightarrow A\cup B=A$ is possible only when all the elements of $B$ are also the elements of $A$ or both $A$ and $B$ have same elements.

$\therefore A\cup B=A$ is possible only when $B\subseteq A$.