Worksheet: Universal Set

In this worksheet, we will practice finding the suitable universal set for two or more given sets.

Q1:

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

  • AOdd numbers set
  • BUniversal set
  • CEven numbers set
  • DPrime numbers set

Q2:

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

  • A 𝑈 is the set of science teachers in the school.
  • B 𝑈 is the set of all teachers in the school.
  • C 𝑈 is the set of math teachers in the school.

Q3:

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

  • A { 0 }
  • B 𝑈
  • C 𝐴
  • D

Q4:

If 𝑌={,,,}𝑈WashingtonNewYorkCaliforniaHawaii, which of the following is a suitable universal set?

  • A 𝑈 is the set of states of America.
  • B 𝑈 is the set of states of Australia.
  • C 𝑈 is the set of provinces of Canada.
  • D 𝑈 is the set of states of Germany.

Q5:

Given that 𝑋={7,11,22}, 𝑌={1,11,21,22}, and 𝑋 and 𝑌 are subsets of some universal set 𝑈, which of the following could be true?

  • A 𝑈 = { 1 , 7 , 1 1 , 2 1 , 2 2 }
  • B 𝑈 = { 1 , 1 1 , 2 1 }
  • C 𝑈 = { 2 2 }
  • D 𝑈 = { 1 , 7 , 1 1 , 2 1 }

Q6:

If 𝑋={49,51,53,55,}, and 𝑌={45,47,49,51} are subsets of a universal set 𝑈, which of the following could describe 𝑈?

  • A 𝑈 = { 4 5 , 4 9 , 5 5 }
  • B 𝑈 = { 4 5 , 4 7 , 4 9 , 5 1 , 5 3 , 5 5 }
  • C 𝑈 = { 4 5 , 4 7 , 4 9 , 5 1 , 5 3 , 5 5 , }
  • D 𝑈 = { 4 9 , 5 1 }
  • E 𝑈 = { 4 5 , 4 7 , 5 3 , 5 5 }

Q7:

Given that 𝑈 is the universal set, what is 𝑈?

  • A 𝑈
  • B { 0 }
  • C0
  • D

Q8:

Given that 𝑈 is the universal set, what is ?

  • A { 0 }
  • B 𝑈
  • C0
  • D

Q9:

Given 𝑋={3,4,1}, 𝑌={10,8,4}, and the universal set 𝑈={8,4,10,1,3}, find 𝑋𝑌.

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

Q10:

Given 𝑋={6,2}, 𝑌={3,1,2,5}, and a universal set 𝑈={1,6,5,7,3,2}, find 𝑋𝑌.

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

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} and 𝐵={2,3,6}, what is 𝐴𝐵?

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

Q12:

Take the universal set to be the set of even numbers that are less than 16. If 𝐴={2,8,14} and 𝐵={4,8,12,14}, what is 𝐴𝐵?

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

Q13:

What is 𝑈𝑋?

  • A 𝑋
  • B
  • C 𝑋
  • D0

Q14:

Given 𝑋={10,3,9}, 𝑌={10,3}, and a universal set 𝑈={10,7,9,3,8}, find 𝑋𝑌.

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

Q15:

Take the universal set to be the set of numbers between, but not including, 1 and 11. Given that 𝐴={4,7,9,10} and 𝐵={2,5,9}, what is 𝐴𝐵?

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

Q16:

If 𝑋={2,1,4}, 𝑌={4,6,5}, and 𝑈={4,1,2,5,6} where 𝑈 is the universal set, what is 𝑈(𝑋𝑌)?

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

Q17:

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

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

Q18:

Given that 𝑋={4,5,20}, 𝑌={14,17,19,20}, and 𝑋 and 𝑌 are subsets of some universal set 𝑈, which of the following could be true?

  • A 𝑈 = { 4 , 5 , 1 4 , 1 7 , 1 9 , 2 0 }
  • B 𝑈 = { 4 , 5 }
  • C 𝑈 = { 2 0 }
  • D 𝑈 = { 4 , 5 , 1 4 , 1 7 , 1 9 }

Q19:

If 𝑋={71,73,75,77,}, and 𝑌={67,69,71,73} are subsets of a universal set 𝑈, which of the following could describe 𝑈?

  • A 𝑈 = { 6 7 , 7 1 , 7 7 }
  • B 𝑈 = { 6 7 , 6 9 , 7 1 , 7 3 , 7 5 , 7 7 }
  • C 𝑈 = { 6 7 , 6 9 , 7 1 , 7 3 , 7 5 , 7 7 , }
  • D 𝑈 = { 7 1 , 7 3 }
  • E 𝑈 = { 6 7 , 6 9 , 7 5 , 7 7 }

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