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Worksheet: Universal Set

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

Q2:

Given , , and a universal set , find .

  • A
  • B
  • C
  • D
  • E

Q3:

Take the universal set to be the set of numbers between, but not including, 1 and 11. Given that and , what is ?

  • A
  • B
  • C
  • D
  • E

Q4:

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

  • A Odd numbers set
  • B Even numbers set
  • C Prime numbers set
  • D Universal 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 governorates of Libya.
  • 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 Arab countries.

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

Q7:

Given , , and the universal set , find .

  • A
  • B
  • C
  • D

Q8:

What is ?

  • A0
  • B
  • C
  • D

Q9:

Given , , and the universal set , find .

  • A
  • B
  • C
  • D
  • E

Q10:

Given , , and a universal set , find .

  • A
  • B
  • C
  • D

Q11:

Take the universal set to be the set of numbers between (but not including) 1 and 10. Given that and , what is ?

  • A
  • B
  • C
  • D
  • E

Q12:

Take the universal set to be the set of even numbers that are less than 16. If and , what is ?

  • A
  • B
  • C
  • D

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

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

Q15:

Given that is the universal set, what is ?

  • A
  • B
  • C0
  • D

Q16:

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

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

Q17:

Given that is a subset of the universal set , what is ?

  • A
  • B
  • C
  • D

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

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