First slide

Operations on Sets

Question

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

Easy

A

A
B

B
C

$\emptyset$
D

None of these

Solution

$A \cap {(A \cup B)}^{'} = A \cap (A^{'} \cap B^{'}), (∵ {(A \cup B)}^{'} = A^{'} \cap B^{'}))$
$= (A \cap A^{'}) \cap B^{1}, (by associative law)$
$= \emptyset \cap B^{'}, (∵ A \cap A' = \emptyset)$
$= \emptyset$

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