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 }
  • B { 𝑎 } , { 𝑛 } , { 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 = { 1 8 , 1 1 , 3 , 2 } and 𝐵 = { 2 , 1 8 , 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 ( ) y b b y .

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

Q4:

Given that 𝑋 = { 3 3 } , find all its subsets.

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

Q5:

Find a subset of { 1 , 5 } .

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

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 . 1 5 } { 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 𝐵 𝐴 .

  • A
  • B

Q10:

Use or to fill in the gap: { 7 , 4 9 , 1 7 , 2 3 , 1 , 3 , 5 1 } the set of odd numbers.

  • A
  • B

Q11:

Fill in the blank using or : { 5 8 } t h e s e t o f d i g i t s o f 5 , 8 8 2 .

  • A
  • B

Q12:

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

Q13:

Given that { 𝑥 } { 1 , 2 7 } , find the value of 𝑥 .

  • A127
  • B28
  • C271
  • D1 or 27
  • E127 or 271

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

Q16:

If { 2 0 , 1 8 , 9 } { 2 0 , 1 8 , 𝑥 } , what are the possible values of 𝑥 ?

  • A 𝑥 can be any number other than 47.
  • B20 or 18 or 9
  • C9
  • D 𝑥 can be any number other than 20, 18, and 9.

Q17:

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

  • A6
  • B6 or 5
  • C 𝑥 can be any number other than 11.
  • D 𝑥 can be any number other than 6 or 5.
  • E 𝑥 can be any number other than 1.

Q18:

Given that { 𝑥 , 3 } { 1 1 , 5 , 𝑦 } , what are the possible values for 𝑥 and 𝑦 ?

  • A 𝑥 = 1 6 , 𝑦 = 3
  • B 𝑦 = 1 1 or 𝑦 = 5 , 𝑥 = 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 } { 7 , 4 , 1 , 3 }
  • C { 3 , 4 , 1 } { 4 , 3 , 1 }
  • D { 3 , 4 , 1 } { 7 , 2 , 5 , 9 }

Q20:

Pick the true statement.

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

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: 1 7 4 .

  • 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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