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 }
  • B { 1 , 3 , 5 , 1 5 }
  • C { 2 , 6 , 1 0 , 3 0 , 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 , 1 0 , 7 , 0 , 3 } , and 𝑋 = { 0 , 3 } , what is 𝑋 ?

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

Q4:

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

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

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 𝑋 𝑌 .

  • A { 2 }
  • B 5 , 9 , 4
  • C 2
  • D { 5 , 4 , 9 }
  • E { 2 , 5 , 9 }

Q8:

Given 𝑋 = { 6 , 1 0 , 3 } , 𝑌 = { 6 , 2 , 3 } , and a universal set 𝑈 = { 3 , 1 0 , 6 , 2 } , find ( 𝑋 𝑌 ) .

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

Q9:

Given 𝑋 = { 8 , 5 } , 𝑌 = { 4 , 5 } , and a universal set 𝑈 = { 1 0 , 8 , 4 , 5 } , find 𝑋 𝑌 .

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

Q10:

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

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

Q11:

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

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

Q12:

If the universal set 𝑈 = { 9 , 1 , 6 , 1 0 } , 𝑋 = { 9 , 6 } , and 𝑌 = { 1 0 , 1 , 6 } , what is ( 𝑋 𝑌 ) ?

  • A { 1 , 9 , 1 0 }
  • B 6
  • C 1 , 9 , 1 0
  • 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 ( 𝐴 𝐵 ) ?

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

Q14:

Given 𝐴 = { 9 , 1 1 , 1 5 } and 𝐵 = { 7 , 9 , 1 1 } belong to a universal set 𝑈 which is the set of odd numbers less than 17, what is ( 𝐴 𝐵 ) ?

  • A { 7 , 9 , 1 1 , 1 5 }
  • B { 1 , 3 , 5 , 7 , 1 3 , 1 5 }
  • C { 1 , 3 , 5 , 7 , 1 3 }
  • 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 , 1 0 , 1 2 } and 𝐵 = { 2 , 6 , 1 4 } , find ( 𝐴 𝐵 ) .

  • A { 6 }
  • B { 4 }
  • C { 2 , 4 , 1 4 }
  • D { 0 , 2 , 4 , 8 , 1 0 , 1 2 , 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 ( 𝐴 𝐵 ) ?

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

Q17:

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

  • A { 9 , 8 , 1 }
  • B 9
  • C 9 , 8 , 1
  • D { 9 }
  • E { 5 }

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 , 1 0 } , what is 𝐴 𝐵 ?

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

Q19:

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

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

Q20:

Given 𝑋 = { 9 , 8 , 1 0 } , 𝑌 = { 1 0 , 9 } , and a universal set 𝑈 = { 3 , 9 , 1 0 , 8 } , find 𝑋 𝑌 .

  • A { 8 , 3 }
  • B 8
  • C 8 , 3
  • D { 8 }
  • E { 9 , 1 0 }

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 𝐴 𝐵 ?

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

Q22:

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

  • A { 4 , 3 }
  • B { 6 , 9 }
  • C { 8 , 5 , 4 , 3 }
  • D { 5 , 4 }
  • 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 𝑋 𝑌 ?

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

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 { 1 , 2 , 4 , 5 , 8 , 1 0 , 2 0 , 4 0 }
  • B { 1 , 2 }
  • C { 4 , 5 , 8 , 1 0 , 2 0 , 4 0 , 1 }
  • D { 4 , 5 , 8 , 1 0 , 2 0 , 4 0 }
  • E { 5 , 8 , 1 0 , 2 0 , 4 0 }

Q25:

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

  • A
  • B
  • C
  • D

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