Question

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

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

Answer 1

The correct option is C $A\cap C$

From the distributive law for three sets:
$A\cap (B\cup C)=(A\cap B)\cup (A\cap C)$
Given $A\cap B=\varnothing$
$\Rightarrow (A\cap B)\cup (A\cap C)=\varnothing \cup (A\cap C)$
$\Rightarrow A\cap (B\cup C)=\varnothing \cup (A\cap C)=A\cap C$