First slide

Operations on Sets

Question

Which is the simplified representation of $(A^{'} \cap B^{'} \cap C) \cup (B \cap C) \cup (A \cap C)$ where A, B and C are subsets of set X?

Moderate

A

A
B

B
C

C
D

$X \cap (A \cup B \cup C)$

Solution

$\begin{array}{l} [(A^{'} \cap B^{'} \cap C)] \cup [(B \cap C) \cup (A \cap C)] \\ = [(A \cup B)^{'} \cap C)] \cup [(B \cup A) \cap C] \\ = [(A \cup B)^{'} \cup (B \cup A)] \cap C \\ = X \cap C \\ = C \end{array}$

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