Worksheet: Complements of a Set

In this worksheet, we will practice finding the complement of a set and using it to perform operations on sets.

Q1:

If the universal set, 𝑈, is the set of factors of the number 30, what is ?

  • A{2,6,10,30,15}
  • B{2,6,10,30}
  • C{1,3,5,15}
  • D{1,2,3,5,6,10,15,30}
  • E{6,10,30}

Q2:

If the universal set is 𝑈={6,10,7,0,3}, and 𝑋={0,3}, what is 𝑋?

  • A6,10,7
  • B{6,10}
  • C{6,10,3}
  • D{6,10,7}
  • E6,10,3

Q3:

If 𝐴 is a subset of a universal set 𝑈, what is 𝐴?

  • A𝑈
  • B{0}
  • C
  • D𝐴

Q4:

Given 𝑋={2,6}, 𝑌={6,4,9}, and a universal set 𝑈={2,3,6,8,4,9}, find 𝑋𝑌.

  • A3,8
  • B{6,9,4,2}
  • C{3,8}
  • D4,2,6,9

Q5:

What is ?

  • A
  • B
  • C
  • D

Q6:

What is ?

  • A
  • B
  • C
  • D

Q7:

Given 𝑋={2,4}, 𝑌={4,5}, and a universal set 𝑈={5,4,2,9}, find 𝑋𝑌.

  • A5,9,4
  • B{5,4,9}
  • C2
  • D{2}
  • E{2,5,9}

Q8:

Given 𝑋={6,10,3}, 𝑌={6,2,3}, and a universal set 𝑈={3,10,6,2}, find (𝑋𝑌).

  • A3,6
  • B{10,2}
  • C{6,3}
  • D{2}
  • E10,2

Q9:

Given 𝑋={8,5}, 𝑌={4,5}, and a universal set 𝑈={10,8,4,5}, find 𝑋𝑌.

  • A5,8,10
  • B{10}
  • C10,8,4,5
  • D{4}
  • E{5,8,10}

Q10:

Given 𝑋={0,9,7}, 𝑌={8,0,9}, and a universal set 𝑈={9,7,8,0}, find 𝑋𝑌.

  • A0,7,9
  • B{8}
  • C{0,9,7}
  • D8

Q11:

If the universal set is 𝑈={9,3,5,0,6,2}, 𝑋={5,6,2}, and 𝑌={2,9}, what is 𝑋𝑌?

  • A{0,3}
  • B{5,6}
  • C{9,2,3,0}
  • D{5,2,6,9}

Q12:

If the universal set 𝑈={9,1,6,10}, 𝑋={9,6}, and 𝑌={10,1,6}, what is 𝑋𝑌?

  • A{1,9,10}
  • B1,9,10
  • C{6}
  • D6

Q13:

Take the universal set to be the set of numbers between, but not including, 1 and 12. Given that 𝐴={4,6,7} and 𝐵={2,3,4,5,6,9}, what is (𝐴𝐵)?

  • A{2,3,4,5,6,7,9}
  • B{2,3,5,7,8,9,10,11}
  • C{2,3,4,5,6,8,9,10,11}
  • D{4,6}

Q14:

Given 𝐴={9,11,15} and 𝐵={7,9,11} belong to a universal set 𝑈 which is the set of odd numbers less than 17, what is (𝐴𝐵)?

  • A{1,3,5,7,13}
  • B{1,3,5,7,13,15}
  • C{7,9,11,15}
  • D{1,3,5,13}

Q15:

Take the universal set to be the set of even numbers less than 15. Given that 𝐴={6,8,10,12} and 𝐵={2,6,14}, find (𝐴𝐵).

  • A{4}
  • B{0,2,4,8,10,12,14}
  • C{6}
  • D{2,4,14}

Q16:

Take the universal set to be the set of integers between, but not including, 1 and 11. Given that 𝐴={2,5,6,7} and 𝐵={4,6,7}, what is (𝐴𝐵)?

  • A{3,8,9,10}
  • B{6,7}
  • C{2,4,5,6,7}
  • D{4}

Q17:

Given 𝑋={0,2,5}, 𝑌={9,5}, and a universal set 𝑈={5,8,9,2,1,0}, find 𝑋𝑌.

  • A{9}
  • B9
  • C9,8,1
  • D{5}
  • E{9,8,1}

Q18:

Take the universal set to be the set of numbers between, but not including, 1 and 12. Given that 𝐴={2,3,4,8} and 𝐵={5,6,9,10}, what is 𝐴𝐵?

  • A{5,6,9,10}
  • B{5,6,7,9,10,11}
  • C
  • D{7,11}
  • E{2,3,4,8}

Q19:

Given that 𝑋={9,2,7},𝑌={8,2,7}, and 𝑋𝑌={5,0}, find 𝑋𝑌.

  • A{9,8}
  • B{5,0,8,2,7}
  • C{8}
  • D{5,0,9,2,7}
  • E{9}

Q20:

Given 𝑋={9,8,10}, 𝑌={10,9}, and a universal set 𝑈={3,9,10,8}, find 𝑋𝑌.

  • A{8}
  • B8,3
  • C8
  • D{9,10}
  • E{8,3}

Q21:

Take the universal set to be the set of numbers between, but not including, 1 and 10. If 𝐴={3,5,8} and 𝐵={5,6,7,8}, what is 𝐴𝐵?

  • A{6,7}
  • B{5,8}
  • C{2,3,4,6,7,9}
  • D{2,4,9}
  • E{3}

Q22:

Given that 𝑋={8,5,4}, 𝑌={3,5,4}, and 𝑋𝑌={6,9}, find 𝑋𝑌.

  • A{8,5,4,3}
  • B{5,4}
  • C{6,9}
  • D{4,3}
  • E{6,9,4,3}

Q23:

If the universal set 𝑈={0,6,9,3,8}, 𝑋={3,8,6}, and 𝑌={8,3}, what is 𝑋𝑌?

  • A{8,3,6}
  • B
  • C{9,0}
  • D{8,3}

Q24:

Take the universal set to be the set of factors of the number 40. Given that 𝐴 is the set of factors of the number 2, find 𝐴.

  • A{4,5,8,10,20,40}
  • B{1,2}
  • C{5,8,10,20,40}
  • D{4,5,8,10,20,40,1}
  • E{1,2,4,5,8,10,20,40}

Q25:

Use , , , or to fill in the gap: If 𝑎𝑋, then 𝑎𝑋.

  • A
  • B
  • C
  • D

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.