Sets 3

A group of 40 students is surveyed. 18 students play tennis (set T), and 6 students play both tennis (T) and basketball (B). What is the number of students who play both tennis and basketball, n(T ∩ B)?

In a club of 50 members, 32 members play chess (set C), 19 members play cards (set D), and 7 members play both chess and cards. Use set notation to calculate the number of members who play only chess.

Set A = {students who play guitar}, Set B = {students who play piano}, in a class of 28 students. Explain using set notation how you would find the number of students who play either guitar or piano, but not both.

In a survey of 60 people:

• 36 people like apples (A),

• 24 people like bananas (B),

• 12 people like both apples and bananas.

A person is chosen at random from the survey.

The Venn diagram below shows information about a class of 50 students and whether they have a pet cat (C) or a pet dog (D).

Let S = {students who play a musical instrument}, U = {all students in class}. Write, in set notation, the set of students who do not play a musical instrument.

In a class, n(A) = 18, n(B) = 12, and n(A ∩ B) = 5. Find n(A ∪ B).