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?

  • A Odd numbers set
  • B Even numbers set
  • C Prime numbers set
  • D Universal 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 math teachers in the school.
  • C 𝑈 is the set of all teachers in the school.

Q3:

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

  • A
  • B { 0 }
  • C 𝐴
  • D 𝑈

Q4:

If 𝑌 = { , , , } 𝑈 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 𝑈 is the set of governorates of Libya.
  • B 𝑈 is the set of governorates of Egypt.
  • C 𝑈 is the set of governorates of Somalia.
  • D 𝑈 is the set of Arab countries.

Q5:

Given that 𝑋 = { 7 , 1 1 , 2 2 } , 𝑌 = { 1 , 1 1 , 2 1 , 2 2 } , 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 }
  • B 𝑈 = { 2 2 }
  • C 𝑈 = { 1 , 1 1 , 2 1 }
  • D 𝑈 = { 1 , 7 , 1 1 , 2 1 , 2 2 }

Q6:

If 𝑋 = { 4 9 , 5 1 , 5 3 , 5 5 , } , and 𝑌 = { 4 5 , 4 7 , 4 9 , 5 1 } are subsets of a universal set 𝑈 , which of the following could describe 𝑈 ?

  • A 𝑈 = { 4 9 , 5 1 }
  • B 𝑈 = { 4 5 , 4 7 , 4 9 , 5 1 , 5 3 , 5 5 }
  • C 𝑈 = { 4 5 , 4 7 , 5 3 , 5 5 }
  • D 𝑈 = { 4 5 , 4 7 , 4 9 , 5 1 , 5 3 , 5 5 , }
  • E 𝑈 = { 4 5 , 4 9 , 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
  • B { 0 }
  • C0
  • D 𝑈

Q9:

Given 𝑋 = { 3 , 4 , 1 } , 𝑌 = { 1 0 , 8 , 4 } , and the universal set 𝑈 = { 8 , 4 , 1 0 , 1 , 3 } , find 𝑋 𝑌 .

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

Q10:

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

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

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 𝐴 𝐵 ?

  • A { 3 , 4 , 5 , 7 , 8 , 9 }
  • B { 2 , 3 , 5 , 6 , 7 , 8 }
  • C { 2 , 3 , 4 , 6 , 9 }
  • D { 2 , 4 , 5 , 6 , 7 , 8 , 9 }
  • E { 4 , 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 𝐵 = { 4 , 8 , 1 2 , 1 4 } , what is 𝐴 𝐵 ?

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

Q13:

What is 𝑈 𝑋 ?

  • A0
  • B 𝑋
  • C
  • D 𝑋

Q14:

Given 𝑋 = { 1 0 , 3 , 9 } , 𝑌 = { 1 0 , 3 } , and a universal set 𝑈 = { 1 0 , 7 , 9 , 3 , 8 } , find 𝑋 𝑌 .

  • A { 8 , 7 }
  • B 7 , 8 , 9
  • C { 9 , 1 0 , 3 }
  • D { 7 , 8 , 9 }
  • 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 , 1 0 } and 𝐵 = { 2 , 5 , 9 } , what is 𝐴 𝐵 ?

  • A { 2 , 3 , 5 , 6 , 8 , 9 }
  • B { 2 , 4 , 5 , 7 , 9 , 1 0 }
  • C { 3 , 4 , 6 , 7 , 8 , 9 , 1 0 }
  • D { 2 , 3 , 4 , 5 , 6 , 7 , 8 , 1 0 }
  • 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 ( 𝑋 𝑌 ) ?

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

Q17:

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

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

Q18:

Given that 𝑋 = { 4 , 5 , 2 0 } , 𝑌 = { 1 4 , 1 7 , 1 9 , 2 0 } , 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 }
  • B 𝑈 = { 2 0 }
  • C 𝑈 = { 4 , 5 }
  • D 𝑈 = { 4 , 5 , 1 4 , 1 7 , 1 9 , 2 0 }

Q19:

If 𝑋 = { 7 1 , 7 3 , 7 5 , 7 7 , } , and 𝑌 = { 6 7 , 6 9 , 7 1 , 7 3 } are subsets of a universal set 𝑈 , which of the following could describe 𝑈 ?

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

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