Question

The set $(A\cup B^{\prime }{)}^{\prime }\cup (B\cap C)$ is equal to

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

Answer 1

The correct option is B

$A^{\prime }\cup B$

We know that,

$(A\cup B{)}^{\prime }=(A^{\prime }\cup B^{\prime }\left)and\right(A^{\prime }{)}^{\prime }=A$

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

=$\left[\right(A^{\prime }\cup B^{\prime }{)}^{\prime }]\cup (B\cap C)$

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