Worksheet: Subsets of a Set

In this worksheet, we will practice finding a subset of a given set and determining whether a given subset belongs to a certain set or not.

Q1:

Find all the subsets of 𝑋={𝑎,𝑛}.

  • A { 𝑎 } , { 𝑛 } , { 𝑎 , 𝑛 }
  • B , { 𝑎 } , { 𝑛 }
  • C , { 𝑎 𝑛 } , { 𝑛 𝑎 } , { 𝑎 , 𝑛 }
  • D , { 𝑎 } , { 𝑛 } , { 𝑎 , 𝑛 }
  • E , { 𝑎 } , { 𝑛 } , { 𝑎 𝑛 } , { 𝑛 𝑎 } , { 𝑎 , 𝑛 }

Q2:

Given that 𝐴={18,11,3,2} and 𝐵={2,18,3}, what is the relation between 𝐴 and 𝐵?

  • A 𝐵 𝐴
  • B 𝐴 𝐵
  • C 𝐵 𝐴
  • D 𝐵 = 𝐴

Q3:

Find all the subsets of the set of the letters of ()ybby.

  • A , { } y b , { } b y , { , } y b
  • B , { } y , { } b , { , } y b
  • C , { } y , { } b , { } y b , { } b y , { , } y b
  • D , { } y , { } b
  • E { } y , { } b , { , } y b

Q4:

Given that 𝑋={33}, find all its subsets.

  • A { 3 } , { 3 3 }
  • B , { 3 } , { 3 3 }
  • C , { 3 3 }
  • D , { 3 }

Q5:

Find a subset of {1,5}.

  • A { 1 , 5 }
  • B { 5 , 8 }
  • C { 7 }
  • D { 1 , 5 , 8 }

Q6:

Use or to fill in the gap: {3}{3,4}.

  • A
  • B

Q7:

Use or to fill in the gap: {5,1,7}{1,9,3}.

  • A
  • B

Q8:

Use or to fill in the gap: {4.15}{5,4,1}.

  • A
  • B

Q9:

Use or to fill in the gap: If 𝐴={5,3,1,6} and 𝐵={6,8,9,5}, then 𝐵𝐴.

  • A
  • B

Q10:

Use or to fill in the gap: {7,49,17,23,1,3,51} the set of odd numbers.

  • A
  • B

Q11:

Fill in the blank using or : {58}5,882thesetofdigitsof.

  • A
  • B

Q12:

Given that {8,7}{9,8,𝑥}, find the value of 𝑥.

Q13:

Given that {𝑥}{1,27}, find the value of 𝑥.

  • A127 or 271
  • B1 or 27
  • C271
  • D127
  • E28

Q14:

Given that {7,𝑥,3} the set of digits of 7,233, find the value of 𝑥.

Q15:

Given that {𝑥,2}{9,2,6} and {1,𝑥,4}{1,6,4,3}, find the value of 𝑥.

  • A 𝑥 = 9
  • B 𝑥 = 6 or 𝑥=3
  • C 𝑥 = 6
  • D 𝑥 = 9 or 𝑥=6
  • E 𝑥 = 3

Q16:

If {20,18,9}{20,18,𝑥}, what are the possible values of 𝑥?

  • A 𝑥 can be any number other than 47.
  • B 𝑥 can be any number other than 20, 18, and 9.
  • C9
  • D20 or 18 or 9

Q17:

If {6}{𝑥,5}, what are the possible values of 𝑥?

  • A6
  • B 𝑥 can be any number other than 11.
  • C6 or 5
  • D 𝑥 can be any number other than 1.
  • E 𝑥 can be any number other than 6 or 5.

Q18:

Given that {𝑥,3}{11,5,𝑦}, what are the possible values for 𝑥 and 𝑦?

  • A 𝑦 = 1 1 or 𝑦=5, 𝑥=3
  • B 𝑥 = 1 6 , 𝑦 = 3
  • C 𝑥 = 6 , 𝑦 = 3
  • D 𝑥 = 1 1 or 𝑥=5, 𝑦=3

Q19:

Pick the true statement.

  • A { 3 , 4 , 1 } { 1 , 4 , 3 , 7 , 2 }
  • B { 3 , 4 , 1 } { 4 , 3 , 1 }
  • C { 3 , 4 , 1 } { 7 , 4 , 1 , 3 }
  • D { 3 , 4 , 1 } { 7 , 2 , 5 , 9 }

Q20:

Pick the true statement.

  • A { 3 , 2 , 5 } { 2 , 5 , 4 }
  • B { 3 , 2 , 5 } { 3 , 2 , 1 , 4 , 7 , 8 }
  • C { 3 , 2 , 5 } { 1 , 2 , 5 , 3 }
  • D { 3 , 2 , 5 } { 3 , 2 }

Q21:

𝐴 = { 5 , 4 , 7 } , 𝐵 = { 7 , 4 , 5 , 3 } , and 𝐶 is the set of digits of the number 547. which statement is correct?

  • A 𝐴 𝐵 , 𝐴 𝐶
  • B 𝐴 𝐵 , 𝐴 𝐶
  • C 𝐴 𝐵 , 𝐴 𝐶
  • D 𝐴 𝐵 , 𝐴 𝐶

Q22:

Which of the following is true?

  • A { 2 . 8 }
  • B { 2 . 8 }

Q23:

Which of the following is true?

  • A { 1 8 + | 2 0 | }
  • B { 1 8 + | 2 0 | }
  • C { 1 8 + | 2 0 | }

Q24:

Use or to complete the following: 174.

  • A
  • B

Q25:

Which of the following is true?

  • A { 2 5 , 1 . 4 }
  • B { 2 5 , 1 . 4 }
  • C { 2 5 , 1 . 4 }

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