First slide

Operations on Sets

Question

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

Moderate

A

$A \cup B \cup C$
B

$A \cap B \cup C$
C

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

$A \cap (B \cup C)$

Solution

$(A - B) \cup (B - C) \cup (C - A) is the shaded portion.$
$∴ [(A - B) \cup (B - C) \cup (C - A)}^{c} is the unshaded portion$
$and which is equal to A \cap B \cap C$

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