WAEC 2022 Mathematics · Question 8

Given that A and B are sets such that n(A) = 8, n(B)=12 and n(AnB) =3, find n(AuB).

Options

A.15
B.17
C.20
D.23

Answer: B. 17

Explanation written with AI and checked against the answer key

Analyze the question: You are given the sizes of two sets and the size of their intersection (the elements they share). You need the size of their union (all elements in A or B or both). Concept: When you add n(A) and n(B), the elements in both sets get counted twice. So you subtract the overlap once: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) Solution: n(A ∪ B) = 8 + 12 − 3 n(A ∪ B) = 20 − 3 n(A ∪ B) = 17 Check: Only A has 8 − 3 = 5 elements, only B has 12 − 3 = 9 elements, and both have 3 elements. Total = 5 + 9 + 3 = 17. ✔ Tip: Always remember "add, then subtract the overlap." A common mistake is picking 20 (option C) by forgetting to subtract the intersection. In a Venn diagram, fill in the middle (the intersection) first, then work outward.

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