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