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

Answer: (B)

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