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

$\emptyset$
D

$A \cap B^{c}$

Solution

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

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