WAEC 2020 · Paper 2 · Q1

(a)
If $A = \{\text{multiples of }2\}$ , $B = \{\text{multiples of }3\}$ and $C = \{\text{factors of }6\}$ are subsets of $\mu = \{x : 1 \le x \le 10\}$ , find $A' \cap B' \cap C'$ .
Show the answer
$\{5, 7\}$
(b)
Tickets for a movie premiere cost $18.50 each while the bulk purchase price for 5 tickets is $80.00. If 4 gentlemen decide to get a fifth person to join them so that they can share the bulk purchase price equally, how much would each person save?

Worked solution (try it first)

List the sets in $\mu = \{1, 2, \ldots, 10\}$ : $A = \{2, 4, 6, 8, 10\}$ , $B = \{3, 6, 9\}$ , $C = \{1, 2, 3, 6\}$ .
Complements: $A' = \{1, 3, 5, 7, 9\}$ , $B' = \{1, 2, 4, 5, 7, 8, 10\}$ , $C' = \{4, 5, 7, 8, 9, 10\}$ .
The numbers in all three: $A' \cap B' \cap C' = \{5, 7\}$ .