Question

If $A$ and $B$ are two sets such that $(A-B)\cup B=A$, then

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

Answer 1

The correct option is A $B\subseteq A$

$(A-B)\cup B=A$
$\Rightarrow (A\cap B^C)\cup B=A$
$\Rightarrow (A\cup B)\cap (B^C\cup B)=A$
$\Rightarrow (A\cup B)\cap U=A$
$\Rightarrow A\cup B=A$
$\Rightarrow B\subseteq A$