Question

If A and B are two sets, then $A \cap ( A \cup B ) ^ { \prime }$ is equal to

• A. A
• B. B
• C. $\phi$
• D. None of these

Answer 1

Answer: (C)

$\phi$

Answer 2

$\left( \because ( A \cup B ) ^ { \prime } = A ^ { \prime } \cap B ^ { \prime } \right)$

$= \left( A \cap A ^ { \prime } \right) \cap B ^ { \prime }$, (by associative law)

$\left( \because A \cap A ^ { \prime } = \phi \right)$

$= \phi$.