State what the notation A' means, where A is a subset of the universal set U.
(1)
4
The universal set U has 40 elements. Set A has 24 elements. Find n(A').
(1)
5
Sets A and B are disjoint (they have no elements in common) within a class of 35 pupils. n(A) = 12 and n(B) = 9. Find n(A u B).
(1)
6
In a group of 30 students, 20 are in set A and 15 are in set B. 8 students are in both A and B. Work out n(A u B).
(2)
7
n(U) = 50, n(A) = 22, n(B) = 19, n(A n B) = 7. Find n(A u B).
(2)
8
In a survey of 60 people, n(A) = 28, n(B) = 25 and n(A n B) = 10. Find the number of people in neither A nor B.
(2)
9
In a group of 45 pupils, 26 like maths (M) and 21 like science (S). 9 pupils like both subjects. Find the number of pupils who like exactly one of the two subjects (not both).
(2)
10
n(U) = 80 and n(A') = 35. Find n(A).
(2)
11
In a class of 32 pupils, every pupil is in set P only, set Q only, both P and Q, or neither. 14 are in P only, 10 are in Q only, 5 are in both P and Q, and 3 are in neither. Find n(P).
(2)
12
Set A and its complement A' cover the whole universal set U with no other elements. n(A) = 27 and n(A') = 18. Find n(U).
(2)
13
In a group of 50 people, n(A) = 31, n(A n B) = 12 and n(A u B) = 45. Find n(B).
(2)
14
In a survey of 100 people, 55 like tea, 40 like coffee, and 15 like both tea and coffee. Find the probability that a randomly selected person likes neither tea nor coffee, giving your answer as a fraction in simplest form.
(3)
15
In a class of 36 students, 21 play football, 18 play basketball, and 8 play both sports.
(a)Find the number of students who play exactly one of the two sports.(2)
(b)Calculate the probability that a randomly selected student plays exactly one of the two sports, giving your answer as a fraction in simplest form.(2)
16
In a group of 60 students, 6 are in all three clubs: Art, Drama and Music. 14 are in both Art and Drama, 10 are in both Art and Music, and 9 are in both Drama and Music (each of these pairwise totals includes the 6 students in all three).
(a)Find the number of students who are in exactly two of the three clubs (not all three).(2)
(b)Find the probability that a randomly selected student is in exactly two of the three clubs, giving your answer as a fraction in simplest form.(2)
17
In a survey of 200 shoppers, 120 buy bread, 90 buy milk, and 40 buy both bread and milk.
(a)Find the number of shoppers who buy at least one of bread or milk.(2)
(b)Find the probability that a randomly selected shopper buys neither bread nor milk, giving your answer as a fraction in simplest form.(2)
18
In a school of 250 students, 140 study French, 100 study Spanish, and 30 study both languages.
(a)Find the number of students who study exactly one of the two languages.(2)
(b)Find the probability that a randomly selected student studies neither language, giving your answer as a fraction in simplest form.(2)
Mark scheme · KS3.M-P6D Venn Diagrams and Set Notation: Fluency and Exam Drill
Question 1
B1 elements that are in both A and B (intersection) cao
Answer: elements in both A and B
Question 2
B1 elements that are in A or B or both (union) cao
Answer: elements in A or B or both
Question 3
B1 elements in U that are not in A (complement) cao
Answer: elements not in A
Question 4
B1 16 cao
Answer: 16
Question 5
B1 21 cao
Answer: 21
Question 6
M1 20 + 15 - 8 oe
A1 27 cao
Answer: 27
Question 7
M1 22 + 19 - 7 oe
A1 34 cao
Answer: 34
Question 8
M1 n(A u B) = 28 + 25 - 10 = 43
A1 17 cao
Answer: 17
Question 9
M1 maths only = 26 - 9 = 17 and science only = 21 - 9 = 12
A1 29 cao
Answer: 29
Question 10
M1 80 - 35 oe
A1 45 cao
Answer: 45
Question 11
M1 n(P) = P only + both = 14 + 5
A1 19 cao
Answer: 19
Question 12
M1 27 + 18 oe
A1 45 cao
Answer: 45
Question 13
M1 rearranges n(A u B) = n(A) + n(B) - n(A n B) to n(B) = 45 - 31 + 12
A1 26 cao
Answer: 26
Question 14
M1 n(tea u coffee) = 55 + 40 - 15 = 80
M1 neither = 100 - 80 = 20
A1 1/5 cao
Answer: 1/5
Question 15
(a) M1 football only = 21 - 8 = 13 and basketball only = 18 - 8 = 10
(a) A1 23 cao
(a) Answer: 23
(b) M1 23/36 shown
(b) A1 23/36 cao (already simplest form)
(b) Answer: 23/36
Question 16
(a) M1 Art and Drama only = 14 - 6 = 8, Art and Music only = 10 - 6 = 4, Drama and Music only = 9 - 6 = 3