First slide

Operations on Sets

Question

Let U be the universal set and $.$ Then $[(A - B) \cup (B - C) \cup (C - A)]^{'}$ equals

Moderate

A

$A \cup B \cup C$
B

$A \cap B \cap C$
C

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

$A \cap (B \cup C)$

Solution

$A - B \to$ Regions 3 and 5.
$B - C \to$ Regions 2 and 6.
$C - A \to$ Regions 4 and 7.
$∴ (A - B) \cup (B - C) \cup (C - A) \to$ Regions2,3,4,5,6,7
$∴ [(A - B) \cup (B - C) \cup (C - A)]^{'} \to$ Region 1, which is $A \cap B \cap C$

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