Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 6
104 practice questions
Topics covered
Practice questions
71–80 of 104
Question 71
1 mark · Easy
Answer and check →Which of the following is the empty set?
- A.{x : x is an odd number divisible by 2}
- B.{1, 3, 5}
- C.{x : x < 5, x ∈ ℕ}
- D.{a, b, c}
Question 72
3 marks · Easy
Answer and see the solution →The universal set is S = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Let A = {1, 3, 5, 7, 9} and B = {3, 4, 5, 6}.
(a)[1 mark]List the set A ∩ B.
(b)[1 mark]Find n(A ∪ B).
(c)[1 mark]List the set (A ∪ B)′.
Question 73
3 marks · Easy
Answer and see the solution →Write these sets using set-builder notation:
(a)[1 mark]The set of natural numbers greater than 6.
(b)[1 mark]The set of all even numbers.
(c)[1 mark]The set of integers between −2 and 3 (inclusive).
Question 74
2 marks · Easy
Answer and see the solution →In a group of 25 students, 15 play football, 12 play basketball, and 5 play both sports. How many students play neither football nor basketball?
Question 75
3 marks · Easy
Answer and see the solution →Using the Venn diagram below, answer the questions that follow.
Venn diagram: Universal set S = {a, b, c, d, e, f, g}, A = {a, b, c, d}, B = {c, d, e, f}. Shaded region is the overlap of A and B. (a)[1 mark]List all the elements in A ∩ B.
(b)[1 mark]List the elements in A ∪ B.
(c)[1 mark]List the elements not in A or B.
Question 76
3 marks · Easy
Answer and see the solution →On the Venn diagram below, shade the region representing (A′ ∩ B).
(a)[2 marks]Shade the region for (A′ ∩ B) clearly on the diagram.
(b)[1 mark]Describe in words the region you shaded.
Question 77
4 marks · Normal
Answer and see the solution →The universal set is U = {1,2,3,4,5,6,7,8,9,10}. Let A = {x ∈ U : x is even}, B = {x ∈ U : x ≥ 6}.
(a)[2 marks]List the elements of sets A and B.
(b)[2 marks]Find A ∩ B and (A ∪ B)′.
Question 78
2 marks · Normal
Answer and see the solution →Is the statement below true or false? Justify your answer. 'If E and F are sets and E ∩ F = ∅, then E and F have no elements in common.'
Question 79
3 marks · Normal
Answer and see the solution →In a group of 60 students, 34 study French, 29 study Spanish, and 18 study both languages. How many students study at least one of these two languages?
Question 80
2 marks · Normal
Answer and see the solution →Write the set of natural numbers less than 8 in set-builder notation.