JAMB 2003 · UME · Q8

Sets & Venn diagrams

Given $U = \{\text{even numbers between 0 and 30}\}$ , $P = \{\text{multiples of 6 between 0 and 30}\}$ and $Q = \{\text{multiples of 4 between 0 and 30}\}$ , find $(P \cup Q)^c$ .

Worked solution (try it first)

"Between 0 and 30" leaves out 0 and 30, so $U = \{2, 4, 6, \dots, 28\}$ .
$P = \{6, 12, 18, 24\}$ and $Q = \{4, 8, 12, 16, 20, 24, 28\}$ , so $P \cup Q = \{4, 6, 8, 12, 16, 18, 20, 24, 28\}$ .
The complement is the even numbers left over: $(P \cup Q)^c = \{2, 10, 14, 22, 26\}$ , option C.

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