Question

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

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

Answer 1

Answer: (D)

$A \cap B ^ { c }$

Answer 2

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

= $\phi \cup \left( A \cap B ^ { c } \right) = A \cap B ^ { c }$ .