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Lesson: Universal Set

In this lesson, we will learn how to find the suitable universal set for two or more given sets.

Sample Question Videos

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Worksheet • 19 Questions • 2 Videos

Q1:

If 𝑋 is the set of math teachers in a school and π‘Œ is the set of science teachers in the school, which of the following could be the universal set that contains 𝑋 and π‘Œ ?

  • A π‘ˆ is the set of math teachers in the school.
  • B π‘ˆ is the set of all teachers in the school.
  • C π‘ˆ is the set of science teachers in the school.

Q2:

Given 𝑋 = { 1 0 , 3 , 9 } , π‘Œ = { 1 0 , 3 } , and a universal set π‘ˆ = { 1 0 , 7 , 9 , 3 , 8 } , find 𝑋 βˆͺ π‘Œ β€² β€² .

  • A { 7 , 8 , 9 }
  • B 9 , 1 0 , 3
  • C 7 , 8 , 9
  • D { 9 , 1 0 , 3 }
  • E { 8 , 7 }

Q3:

Take the universal set to be the set of numbers between, but not including, 1 and 11. Given that 𝐴 = { 4 , 7 , 9 , 1 0 } β€² and 𝐡 = { 2 , 5 , 9 } β€² , what is 𝐴 βˆͺ 𝐡 ?

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

Q4:

What is the name we give to the set which contains all elements and of which all other sets are subsets?

  • A Universal set
  • B Even numbers set
  • C Prime numbers set
  • D Odd numbers set

Q5:

If π‘Œ = { , , , } βŠ‚ π‘ˆ E g y p t L i b y a S o m a l i a S u d a n , which of these is a suitable universal set?

  • A π‘ˆ is the set of Arab countries.
  • B π‘ˆ is the set of governorates of Egypt.
  • C π‘ˆ is the set of governorates of Somalia.
  • D π‘ˆ is the set of governorates of Libya.

Q6:

If 𝑋 = { 2 , 1 , 4 } , π‘Œ = { 4 , 6 , 5 } , and π‘ˆ = { 4 , 1 , 2 , 5 , 6 } where π‘ˆ is the universal set, what is π‘ˆ βˆ’ ( 𝑋 βˆͺ π‘Œ ) ?

  • A βˆ…
  • B { 4 , 2 , 1 , 6 , 5 }
  • C { 5 , 6 }
  • D 2 , 4 , 1 , 5 , 6

Q7:

Given 𝑋 = { 9 , 8 } , π‘Œ = { 3 , 8 } , and the universal set π‘ˆ = { 6 , 9 , 8 , 3 } , find 𝑋 βˆͺ π‘Œ β€² .

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

Q8:

What is π‘ˆ βˆ’ 𝑋 ?

  • A 𝑋 β€²
  • B 𝑋
  • C βˆ…
  • D0

Q9:

Given 𝑋 = { 3 , 4 , 1 } , π‘Œ = { 1 0 , 8 , 4 } , and the universal set π‘ˆ = { 8 , 4 , 1 0 , 1 , 3 } , find 𝑋 βˆͺ π‘Œ β€² .

  • A { 1 , 3 , 4 }
  • B 1 , 3 , 4 , 8 , 1 0
  • C 3 , 1 , 4
  • D { 1 , 4 , 3 , 1 0 , 8 }
  • E { 4 }

Q10:

Given 𝑋 = { 6 , 2 } , π‘Œ = { 3 , 1 , 2 , 5 } , and a universal set π‘ˆ = { 1 , 6 , 5 , 7 , 3 , 2 } , find 𝑋 βˆͺ π‘Œ β€² β€² .

  • A { 7 , 6 , 3 , 5 , 1 }
  • B 6 , 7 , 1 , 5 , 3
  • C 1 , 6 , 5 , 7 , 3 , 2
  • D { 1 , 6 , 5 , 7 , 3 , 2 }

Q11:

Take the universal set to be the set of numbers between (but not including) 1 and 10. Given that 𝐴 = { 2 , 4 , 6 , 9 } β€² and 𝐡 = { 2 , 3 , 6 } β€² , what is 𝐴 βˆͺ 𝐡 β€² ?

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

Q12:

Take the universal set to be the set of even numbers that are less than 16. If 𝐴 = { 2 , 8 , 1 4 } and 𝐡 = { 4 , 8 , 1 2 , 1 4 } , what is 𝐴 βˆͺ 𝐡 β€² ?

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

Q13:

Given that 𝑋 = { 7 , 1 1 , 2 2 } , π‘Œ = { 1 , 1 1 , 2 1 , 2 2 } , and 𝑋 and π‘Œ are subsets of some universal set π‘ˆ , which of the following could be true?

  • A π‘ˆ = { 1 , 7 , 1 1 , 2 1 , 2 2 }
  • B π‘ˆ = { 2 2 }
  • C π‘ˆ = { 1 , 1 1 , 2 1 }
  • D π‘ˆ = { 1 , 7 , 1 1 , 2 1 }

Q14:

Given that 𝑋 = { 4 , 5 , 2 0 } , π‘Œ = { 1 4 , 1 7 , 1 9 , 2 0 } , and 𝑋 and π‘Œ are subsets of some universal set π‘ˆ , which of the following could be true?

  • A π‘ˆ = { 4 , 5 , 1 4 , 1 7 , 1 9 , 2 0 }
  • B π‘ˆ = { 2 0 }
  • C π‘ˆ = { 4 , 5 }
  • D π‘ˆ = { 4 , 5 , 1 4 , 1 7 , 1 9 }

Q15:

Given that π‘ˆ is the universal set, what is π‘ˆ ?

  • A βˆ…
  • B { 0 }
  • C0
  • D π‘ˆ

Q16:

Given that π‘ˆ is the universal set, what is βˆ… β€² ?

  • A π‘ˆ
  • B { 0 }
  • C0
  • D βˆ…

Q17:

Given that 𝐴 is a subset of the universal set π‘ˆ , what is 𝐴 βˆͺ 𝐴 ?

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

Q18:

If 𝑋 = { 4 9 , 5 1 , 5 3 , 5 5 , … } , and π‘Œ = { 4 5 , 4 7 , 4 9 , 5 1 } are subsets of a universal set π‘ˆ , which of the following could describe π‘ˆ ?

  • A π‘ˆ = { 4 5 , 4 7 , 4 9 , 5 1 , 5 3 , 5 5 , … }
  • B π‘ˆ = { 4 5 , 4 9 , 5 5 }
  • C π‘ˆ = { 4 5 , 4 7 , 4 9 , 5 1 , 5 3 , 5 5 }
  • D π‘ˆ = { 4 5 , 4 7 , 5 3 , 5 5 }
  • E π‘ˆ = { 4 9 , 5 1 }

Q19:

If 𝑋 = { 7 1 , 7 3 , 7 5 , 7 7 , … } , and π‘Œ = { 6 7 , 6 9 , 7 1 , 7 3 } are subsets of a universal set π‘ˆ , which of the following could describe π‘ˆ ?

  • A π‘ˆ = { 6 7 , 6 9 , 7 1 , 7 3 , 7 5 , 7 7 , … }
  • B π‘ˆ = { 6 7 , 7 1 , 7 7 }
  • C π‘ˆ = { 6 7 , 6 9 , 7 1 , 7 3 , 7 5 , 7 7 }
  • D π‘ˆ = { 6 7 , 6 9 , 7 5 , 7 7 }
  • E π‘ˆ = { 7 1 , 7 3 }
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