Question

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

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

Answer 1

Answer: (A)

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