First slide

Operations on Sets

Question

The set ${(A \cap B^{'})}^{'} \cup (B \cap C)$ is equal to

Moderate

A

$A^{'} \cup B \cup C$
B

$A^{'} \cup B$
C

$A^{'} \cup C^{'}$
D

$A^{'} \cap B$

Solution

$\begin{aligned} {(A \cap B^{'})}^{'} \cup (B \cap C) = ((A^{'} \cup {(B^{'})}^{'}) \cup (B \cap C) \\ = (A^{'} \cup B) \cup (C \cap B) \\ = A^{'} \cup (B \cup (C \cap B)) \\ = A^{'} \cup B \end{aligned}$

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