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?

  • A𝑈 is the set of science teachers in the school.
  • B𝑈 is the set of all teachers in the school.
  • C𝑈 is the set of math teachers in the school.

Q3:

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

  • A𝑈 is the set of states of America.
  • B𝑈 is the set of states of Australia.
  • C𝑈 is the set of provinces of Canada.
  • D𝑈 is the set of states of Germany.

Q4:

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?

  • A𝑈={1,7,11,21,22}
  • B𝑈={1,11,21}
  • C𝑈={22}
  • D𝑈={1,7,11,21}

Q5:

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?

  • A𝑈={45,49,55}
  • B𝑈={45,47,49,51,53,55}
  • C𝑈={45,47,49,51,53,55,}
  • D𝑈={49,51}
  • E𝑈={45,47,53,55}

Q6:

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?

  • A𝑈={4,5,14,17,19,20}
  • B𝑈={4,5}
  • C𝑈={20}
  • D𝑈={4,5,14,17,19}

Q7:

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?

  • A𝑈={67,71,77}
  • B𝑈={67,69,71,73,75,77}
  • C𝑈={67,69,71,73,75,77,}
  • D𝑈={71,73}
  • E𝑈={67,69,75,77}

Q8:

If 𝑋={4,7,8}, 𝑌={7,2}, and 𝑈={9,2,4,8,7}, where 𝑈 is the universal set, what is 𝑈(𝑋𝑌)?

  • A{2,9,4,8}
  • B2,9
  • C{7}
  • D4,2,8,9
  • E{2,9}

Q9:

If 𝑋𝑌, what is 𝑋𝑌?

  • A𝑈
  • B𝑋
  • C
  • D𝑌

Q10:

Using the Venn diagram, find 𝑋𝑈.

  • A
  • B{5,0}
  • C{3,6}
  • D{5,0,4,8}
  • E{3,6,5,0}

Q11:

If 𝑋={0,1,9,6}, 𝑌={5,4,9,6}, and 𝑍={3,2} are all subsets of a universal set 𝑈, which Venn diagram represents these sets?

  • A(c)
  • B(d)
  • C(a)
  • D(b)

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