The set \((A \cup B \cup C) \cap (A \cap B′ \cap C′)′ \cup C′\) is equal to
(a) \(B \cap C’\)
(b) \(A \cap C\)
(c) \(B \cup C’\)
(d) \(A \cap C’\)
Solution
\[ (A\cup B\cup C)\cap(A\cap B’\cap C’)’\cup C’ \]
Using De Morgan’s law,
\[ (A\cap B’\cap C’)’=A’\cup B\cup C \]
Therefore,
\[ =(A\cup B\cup C)\cap(A’\cup B\cup C)\cup C’ \]
\[ =(B\cup C)\cup C’ \]
\[ = B\cup(C\cup C’) \]
\[ = B\cup U \]
\[ =U \]
Answer
\[ \boxed{U} \]
Hence, none of the given options is correct.