WAEC 2010 · Paper 2 · Q1

Sets & Venn diagrams

(a)
$A = \{2, 4, 6, 8\}$ , $B = \{2, 3, 7, 9\}$ and $C = \{x : 3 < x < 9\}$ are subsets of the universal set $U = \{2, 3, 4, 5, 6, 7, 8, 9\}$ . Find $A \cap (B' \cap C')$ .
Show the answer
$\varnothing$ (the empty set, $\{\ \}$ )
(b)
Find $(A \cup B) \cap (B \cup C)$ .
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

List $C$ first: the whole numbers in $U$ between 3 and 9 are $C = \{4, 5, 6, 7, 8\}$ .
Complements are the members of $U$ not in the set: $B' = \{4, 5, 6, 8\}$ and $C' = \{2, 3, 9\}$ .

(a)

$B'$ and $C'$ have no member in common, so $B' \cap C' = \varnothing$ .
Any set intersected with the empty set is empty: $A \cap (B' \cap C') = \varnothing$ .

(b)

Join the sets: $A \cup B = \{2, 3, 4, 6, 7, 8, 9\}$ and $B \cup C = \{2, 3, 4, 5, 6, 7, 8, 9\}$ .
Keep the members in both: $(A \cup B) \cap (B \cup C) = \{2, 3, 4, 6, 7, 8, 9\}$ .

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