Question

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

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

Answer 1

The correct option is B $A^{\prime }\cup B$

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