For any two sets A and B, \(A \cap (A \cup B)’\) is equal to
(a) \(A\)
(b) \(B\)
(c) \(\phi\)
(d) \(A\cap B\)
Solution
\[ A\cap(A\cup B)’ \]
Using De Morgan’s law,
\[ =A\cap(A’\cap B’) \]
\[ =(A\cap A’)\cap B’ \]
\[ =\phi\cap B’ \]
\[ =\phi \]
Answer
\[ \boxed{\phi} \]
Correct option: (c)