Question:
For any two sets $A$ and $B, A \cap(A \cup B)^{\prime}$ is equal to
(a) A
(b) B
(c) $\phi$
(d) $A \cap B$
Solution:
$A \cap(A \cup B)^{\prime}$
$=A \cap\left(A^{\prime} \cap B^{\prime}\right)$ (De Morgan law)
$=\left(A \cap A^{\prime}\right) \cap B^{\prime}$
$=\phi \cap B^{\prime}$
$=\phi$
Hence, the correct answer is option (c).
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