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Lesson: Complements of a Set

Sample Question Videos

Worksheet • 25 Questions • 2 Videos

Q1:

Given 𝑋 = { 0 , 2 , 5 } , π‘Œ = { 9 , 5 } , and a universal set π‘ˆ = { 5 , 8 , 9 , 2 , 1 , 0 } , find 𝑋 ∩ π‘Œ β€² .

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

Q2:

Take the universal set to be the set of numbers between, but not including, 1 and 12. Given that 𝐴 = { 2 , 3 , 4 , 8 } β€² and 𝐡 = { 5 , 6 , 9 , 1 0 } β€² , what is 𝐴 ∩ 𝐡 β€² ?

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

Q3:

Given 𝑋 = { 2 , 4 } , π‘Œ = { 4 , 5 } , and a universal set π‘ˆ = { 5 , 4 , 2 , 9 } , find ( 𝑋 ∩ π‘Œ ) β€² β€² .

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

Q4:

Given that 𝑋 = { 8 , 5 , 0 } , π‘Œ = { 2 , 5 , 0 } , and 𝑋 ∩ π‘Œ = { 7 , 3 } , find π‘Œ ∩ 𝑋 .

  • A { 8 }
  • B { 7 , 3 , 2 , 5 , 0 }
  • C { 2 }
  • D { 7 , 3 , 8 , 5 , 0 }
  • E { 8 , 2 }

Q5:

Take the universal set to be the set of even numbers less than 15. Given that 𝐴 = { 6 , 8 , 1 0 , 1 2 } and 𝐡 = { 2 , 6 , 1 4 } , find ( 𝐴 ∩ 𝐡 ) β€² .

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

Q6:

Take the universal set to be the set of odd numbers less than 14. Given that 𝐴 = { 3 , 7 , 1 1 , 1 3 } and 𝐡 = { 1 , 3 , 5 , 9 , 1 3 } , find ( 𝐴 ∩ 𝐡 ) β€² .

  • A { 1 , 5 , 7 , 9 , 1 1 }
  • B βˆ…
  • C { 1 , 5 , 9 }
  • D { 3 , 1 3 }

Q7:

Given 𝑋 = { 8 , 5 } , π‘Œ = { 4 , 5 } , and a universal set π‘ˆ = { 1 0 , 8 , 4 , 5 } , find ( 𝑋 βˆͺ π‘Œ ) β€² β€² .

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

Q8:

Given 𝐴 = { 9 , 1 1 , 1 5 } and 𝐡 = { 7 , 9 , 1 1 } belong to a universal set π‘ˆ which is the set of odd numbers less than 17, what is ( 𝐴 βˆͺ 𝐡 ) β€² ?

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

Q9:

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 β€² .

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

Q10:

Given 𝑋 = { 2 , 6 } , π‘Œ = { 6 , 4 , 9 } , and a universal set π‘ˆ = { 2 , 3 , 6 , 8 , 4 , 9 } , find ( 𝑋 ∩ π‘Œ ) β€² β€² β€² .

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

Q11:

Given 𝑋 = { 6 , 1 0 , 3 } , π‘Œ = { 6 , 2 , 3 } , and a universal set π‘ˆ = { 3 , 1 0 , 6 , 2 } , find ( 𝑋 ∩ π‘Œ ) β€² .

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

Q12:

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

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

Q13:

Given 𝑋 = { 9 , 8 , 1 0 } , π‘Œ = { 1 0 , 9 } , and a universal set π‘ˆ = { 3 , 9 , 1 0 , 8 } , find 𝑋 ∩ π‘Œ β€² .

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

Q14:

Take the universal set to be the set of numbers between, but not including, 1 and 10. If 𝐴 = { 3 , 5 , 8 } β€² and 𝐡 = { 5 , 6 , 7 , 8 } β€² , what is 𝐴 ∩ 𝐡 ?

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

Q15:

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

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

Q16:

Given 𝑋 = { 0 , 9 , 7 } , π‘Œ = { 8 , 0 , 9 } , and a universal set π‘ˆ = { 9 , 7 , 8 , 0 } , find ο€Ί 𝑋 ∩ π‘Œ  .

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

Q17:

Given that 𝑋 = { 8 , 5 , 4 } , π‘Œ = { 3 , 5 , 4 } , and 𝑋 ∩ π‘Œ = { 6 , 9 } , find 𝑋 ∩ π‘Œ .

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

Q18:

If the universal set is π‘ˆ = { 6 , 1 0 , 7 , 0 , 3 } , and 𝑋 = { 0 , 3 } , what is 𝑋 ?

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

Q19:

If the universal set is π‘ˆ = { 5 , 7 , 4 , 1 0 , 2 } , and 𝑋 = { 7 , 1 0 , 4 } , what is 𝑋 ?

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

Q20:

What is β„š ∩ β„€ β€² ?

  • A βˆ…
  • B β„€
  • C β„š β€²
  • D β„š

Q21:

What is β„š ∩ β„š β€² ?

  • A βˆ…
  • B β„•
  • C ℝ
  • D β„š

Q22:

If 𝐴 is a subset of a universal set π‘ˆ , what is ( 𝐴 ) β€² β€² ?

  • A 𝐴
  • B βˆ…
  • C { 0 }
  • D π‘ˆ

Q23:

If the universal set is π‘ˆ = { 9 , 3 , 5 , 0 , 6 , 2 } , 𝑋 = { 5 , 6 , 2 } , and π‘Œ = { 2 , 9 } , what is ( 𝑋 βˆͺ π‘Œ ) β€² β€² ?

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

Q24:

If the universal set π‘ˆ = { 9 , 1 , 6 , 1 0 } , 𝑋 = { 9 , 6 } , and π‘Œ = { 1 0 , 1 , 6 } , what is ( 𝑋 βˆͺ π‘Œ ) β€² β€² β€² ?

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

Q25:

If the universal set π‘ˆ = { 0 , 6 , 9 , 3 , 8 } , 𝑋 = { 3 , 8 , 6 } , and π‘Œ = { 8 , 3 } , what is 𝑋 ∩ π‘Œ β€² β€² ?

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