If A and B are two given sets, then A∩(A∩B)c is equal to

A
A
B
B
C
$ϕ$
D
$A \cap B^{c}$

Solution:

$\begin{matrix} A \cap (A \cap B)^{c} = A \cap (A^{c} \cup B^{c}) (∵ by De-Morgan's law) \\ = (A \cap A^{c}) \cup (A \cap B^{c}) \\ = ϕ \cup (A \cap B^{c}) = A \cap B^{c} \end{matrix}$

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