Use everyday occurrences to illustrate set descriptions and representations of events, and set operations, including the use of Venn diagrams.

A school conducts a survey of 150 Year 11 students about their participation in three sporting clubs: Tennis (T), Basketball (B), and Swimming (S). The Venn diagram below shows the distribution of students across these clubs. Which region represents students who participate in exactly two of the three sports?

A survey of 150 students at a school asks about their participation in two sports: basketball and tennis. The data collected shows: • 58 students play basketball • 47 students play tennis • 18 students play both basketball and tennis Determine: (a) The number of students who play basketball only. (b) The number of students who play tennis only. (c) The number of students who play neither sport.

A survey of 240 university students investigated their participation in three extracurricular activities: volunteering \(V\), sports clubs \(S\), and performing arts \(P\). Use the information in the table to determine: (a) the number of students who participate in exactly two of the three activities. (2 marks) (b) the number of students who participate in volunteering but not in sports clubs. (2 marks)