First slide

Operations on Sets

Question

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

Moderate

A

$A$
B

$B$
C

$C$
D

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

Solution

$\begin{array}{l} A^{'} \cap B^{'} \cap C = only C \\ ∴ (A^{'} \cap B^{'} \cap C) \cup (B \cap C) \cup (A \cap C) = C \cup (B \cap C) \cup (A \cap C) = C \end{array}$

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