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 , 1 0 , 3 0 , 1 5 }
  • B { 2 , 6 , 1 0 , 3 0 }
  • C { 1 , 3 , 5 , 1 5 }
  • D { 1 , 2 , 3 , 5 , 6 , 1 0 , 1 5 , 3 0 }
  • E { 6 , 1 0 , 3 0 }

Q2:

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

  • A 6 , 1 0 , 7
  • B { 6 , 1 0 }
  • C { 6 , 1 0 , 3 }
  • D { 6 , 1 0 , 7 }
  • E 6 , 1 0 , 3

Q3:

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

  • A 𝑈
  • B { 0 }
  • C
  • D 𝐴

Q4:

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

  • A 3 , 8
  • B { 6 , 9 , 4 , 2 }
  • C { 3 , 8 }
  • D 4 , 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.

  • A 5 , 9 , 4
  • B { 5 , 4 , 9 }
  • C 2
  • 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).

  • A 3 , 6
  • B { 1 0 , 2 }
  • C { 6 , 3 }
  • D { 2 }
  • E 1 0 , 2

Q9:

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

  • A 5 , 8 , 1 0
  • B { 1 0 }
  • C 1 0 , 8 , 4 , 5
  • D { 4 }
  • E { 5 , 8 , 1 0 }

Q10:

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

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

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 , 1 0 }
  • B 1 , 9 , 1 0
  • C { 6 }
  • D 6

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 , 1 0 , 1 1 }
  • C { 2 , 3 , 4 , 5 , 6 , 8 , 9 , 1 0 , 1 1 }
  • 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 , 1 3 }
  • B { 1 , 3 , 5 , 7 , 1 3 , 1 5 }
  • C { 7 , 9 , 1 1 , 1 5 }
  • D { 1 , 3 , 5 , 1 3 }

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 , 1 0 , 1 2 , 1 4 }
  • C { 6 }
  • D { 2 , 4 , 1 4 }

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 , 1 0 }
  • 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 }
  • B 9
  • C 9 , 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 , 1 0 }
  • B { 5 , 6 , 7 , 9 , 1 0 , 1 1 }
  • C
  • D { 7 , 1 1 }
  • 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 }
  • B { 9 , 1 0 }
  • C { 8 , 3 }
  • D 8
  • 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 , 1 0 , 2 0 , 4 0 }
  • B { 1 , 2 }
  • C { 5 , 8 , 1 0 , 2 0 , 4 0 }
  • D { 4 , 5 , 8 , 1 0 , 2 0 , 4 0 , 1 }
  • E { 1 , 2 , 4 , 5 , 8 , 1 0 , 2 0 , 4 0 }

Q25:

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

  • A
  • B
  • C
  • D

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