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Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter

Sets

20 practice questions

Start practising (20 questions)

Practice questions

11–20 of 20

  1. Question 11

    4 marks · Normal

    In a survey, 35 students were asked if they play football (F) or tennis (T).

    Results
    CategoryNumber of students
    Play only football15
    Play only tennis12
    Play both sports5
    Play neither3
    (a)

    How many students play football?

    [1 mark]
    (b)

    How many students play tennis?

    [1 mark]
    (c)

    How many play exactly one sport?

    [1 mark]
    (d)

    Verify that the total number of students is 35.

    [1 mark]
    Answer and see the solution →

  2. Question 12

    3 marks · Normal

    The Venn diagram shows sets E and F in a universal set S.

    Geometry diagram with points E, F
    Venn diagram for question 6.
    (a)

    What name is given to the overlapping part of E and F?

    [1 mark]
    (b)

    Write the symbol or notation for the region that is inside E or inside F or both.

    [1 mark]
    (c)

    Write in set notation the region outside both E and F.

    [1 mark]
    Answer and see the solution →

  3. Question 13

    4 marks · Normal

    Let and .

    (a)

    List all the elements in .

    [2 marks]
    (b)

    List all the elements in .

    [1 mark]
    (c)

    List all the elements in , if the universal set is .

    [1 mark]
    Answer and see the solution →

  4. Question 14

    2 marks · Normal

    State whether the following statement is true or false: If is an element of both sets and , then .

    Answer and see the solution →

  5. Question 15

    4 marks · Normal

    Let the universal set . Set and set .

    (a)

    List the elements of .

    [1 mark]
    (b)

    List the elements of .

    [1 mark]
    (c)

    Write down , the complement of set in .

    [1 mark]
    (d)

    Describe, using set notation, the set of elements in that belong to but not to .

    [1 mark]
    Answer and see the solution →

  6. Question 16

    3 marks · Normal

    Write down the meaning of these three symbols as used in set notation: (a) (b) (c) (the prime symbol as in )

    Answer and see the solution →

  7. Question 17

    4 marks · Normal

    The Venn diagram below represents sets and in the universal set .

    Geometry diagram with points A, B2358
    Venn diagram showing sets X and Y within U. Each region labelled with numbers.
    (a)

    List the elements of set .

    [1 mark]
    (b)

    List the elements of set .

    [1 mark]
    (c)

    Write down the elements of .

    [1 mark]
    (d)

    List the elements in that are not in or .

    [1 mark]
    Answer and see the solution →

  8. Question 18

    4 marks · Hard

    In a class of 30 students, the universal set U consists of all the students. Let set M be the students who play music (18 students), set S be the students who play sports (15 students), and 8 students play both music and sports.

    (a)

    How many students play only music?

    [1 mark]
    (b)

    How many students play neither music nor sports?

    [2 marks]
    (c)

    Represent this information in a Venn diagram. Clearly label all sets and indicate the number of students in each region.

    [1 mark]
    Answer and see the solution →

  9. Question 19

    2 marks · Hard

    Describe, using set notation, the difference between the sets and . Give an example with sets A = \{apple, banana\} and B = \{banana, cherry\}.

    Answer and see the solution →

  10. Question 20

    3 marks · Hard

    Let the universal set . Let , .

    (a)

    List the elements of P and Q.

    [1 mark]
    (b)

    Find .

    [1 mark]
    (c)

    How many elements are in ?

    [1 mark]
    Answer and see the solution →