First slide

Operations on Sets

Question

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

Easy

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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