Mathematics

Problem

Suppose

U = \{x \in \mathbb{Z}^+ \mid x < 40\}

A = \{\text{multiples of } 4 \text{ less than } 40\}

B = \{\text{multiples of } 6 \text{ less than } 40\}

, and

C = \{\text{multiples of } 12 \text{ less than } 40\}

. a. List the sets

A

B

, and

C

. b. Find:


i $A \cap B$	ii $B \cap C$	iii $A \cap C$
iv $A \cap B \cap C$	v $A \cup B \cup C$

c. Show that

n(A \cup B \cup C) = n(A) + n(B) + n(C) - n(A \cap B) - n(B \cap C) - n(A \cap C) + n(A \cap B \cap C)