Question

For three sets $A,B\&C,$ if $A\subset B,A\subset C$ then $A\cap (B\cup C)=$

• A. $A$
• B. $B\cap C$
• C. $B\cup C$

Answer 1

The correct option is A $A$

Given three sets $A,B\&C$ and
$A\subset B\Rightarrow A\cap B=A;A\cup B=B$
Similarly, $A\subset C\Rightarrow A\cap C=A;A\cup C=C$
Now, by distributive property:
$A\cap (B\cup C)=(A\cap B)\cup (A\cap C)$
$\Rightarrow A\cap (B\cup C)=A\cap A=A$