Question

Let $A,B$ are subsets of $U$. Then $(A\cap \{U-B\left\}\right)\cup B$

• A. $A$
• B. $A\cap B$
• C. $A\cup B$
• D. none of these

Answer 1

Answer: (C)

$A\cup B$

Now,

$(A\cap \{U-B\left\}\right)\cup B$

$=(A\cap B^{\prime })\cup B$

$=(A\cup B)\cap (B^{\prime }\cup B)$

$=(A\cup B)\cap U$ [ Since $B^{\prime }\cup B=U$]

$=(A\cup B)$.