BECE Mathematics 2018 Paper

Concept:The intersection of two sets contains only the elements present in both sets. The number of subsets of any set with $n$ elements is given by $2^n$.Explanation:List all factors of 36:$P = \{1,2,3,4,6,9,12,18,36\}$List all multiples of 4 that are less than 40:$Q = \{4,8,12,16,20,24,28,32,36\}$The intersection $P \cap Q$ includes elements common to both lists:$P \cap Q = \{4,12,36\}$So the number of elements in the intersection is $n(P \cap Q)=3$.For a set with $n$ elements, the total number of subsets is $2^n$.Therefore, the number of subsets of $P \cap Q$ is:$2^3 = 2 \times 2 \times 2 = 8$Answer:$8$, i.e., option B.