WAEC Mathematics 2023 Paper

Concept:Use a two-circle Venn diagram and set notation to separate overlapping groups, then get the total class size from the sum of all the regions.Explanation:Let $W$ represent students who study woodwork and $M$ represent students who study metalwork.The total number of students in the class is the universal set, so $\mu = 30$.From the question, $n(W) = 15$, $n(M) = 13$, and $6$ students study neither subject.Let $x$ be the number of students who study both woodwork and metalwork.Students who study woodwork only are $15 - x$.Students who study metalwork only are $13 - x$.Every student belongs to exactly one of these four groups: woodwork only, metalwork only, both subjects, or neither.Summing these four groups gives the total class size: $(15 - x) + (13 - x) + x + 6 = 30$.Simplifying the left side, $34 - x = 30$.Solving, $x = 4$ students take both subjects.Therefore, the number who study woodwork but not metalwork is $15 - x = 15 - 4 = 11$.Answer:$11$ students study woodwork but not metalwork, so the correct option is B.