Question

For any sets $A\&B,A\cup (B-A)=$

• A. $A\cap B$
• B. $A\cup B$
• C. $\varnothing$
• D. $A^{\prime }\cap B$

Answer 1

The correct option is B $A\cup B$

Given two sets $A\&B$
Now, $A\cup (B-A)=A\cup (B\cap A^{\prime })$
$=(A\cup B)\cap (A\cup A^{\prime })$
Since, $A\cup A^{\prime }=U$
$\Rightarrow A\cup (B-A)=(A\cup B)\cap U$
$\Rightarrow A\cup (B-A)=(A\cup B)$