A theatre offers a singing lesson (S), a dancing lesson (D) and an acting lesson (A). A group of 40 people are asked which lessons they take part in. Some of the results are shown in the Venn diagram. [Figure with Venn diagram showing sets S, D, A with numbers 6, 10, 3 (outside of A) and an empty box labelled 0]

1. (a)All 40 people take part in at least one lesson. 3 people take part in a singing lesson and an acting lesson but not a dancing lesson. 7 people take part in a dancing lesson only. 19 people take part in a singing lesson. 4 times as many people take part in a singing lesson only as those who take part in all three lessons. Use this information to complete the Venn diagram.[3]
2. (b)Use set notation to describe the subset with 10 people.[1]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.