JAMB 1992 · UME · Q9

Sets & Venn diagrams

If $U = \{0, 2, 3, 6, 7, 8, 9, 10\}$ is the universal set, $E = \{0, 4, 6, 8\}$ and $F = \{x : x^2 = 2^6, x \text{ is odd}\}$ , find $(E \cap F)'$ , where $'$ means the complement of a set.

Worked solution (try it first)

$x^2 = 2^6 = 64$ gives $x = 8$ or $x = -8$ .
Neither is odd, so $F = \varnothing$ .
Nothing is in both $E$ and an empty set, so $E \cap F = \varnothing$ .
The complement of the empty set is everything in the universal set: $(E \cap F)' = U$ , option B.

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