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Worksheet: Subsets of a Set

Q1:

Given that 𝐴 = { 1 8 , 1 1 , 3 , 2 } and 𝐡 = { 2 , 1 8 , 3 } , what is the relation between 𝐴 and 𝐡 ?

  • A 𝐡 βŠ„ 𝐴
  • B 𝐴 βŠ‚ 𝐡
  • C 𝐡 = 𝐴
  • D 𝐡 βŠ‚ 𝐴

Q2:

Which of the following is true?

  • A { 2 . 8 } βŠ„ β„€
  • B { 2 . 8 } βŠ‚ β„€

Q3:

Given that { 7 , π‘₯ , 3 } βŠ‚ the set of digits of 7 233, find the value of π‘₯ .

Q4:

If { 2 0 , 1 8 , 9 } βŠ„ { 2 0 , 1 8 , π‘₯ } , what are the possible values of π‘₯ ?

  • A π‘₯ can be any number other than 47.
  • B20 or 18 or 9
  • C9
  • D π‘₯ can be any number other than 20, 18, and 9.

Q5:

Given that { 8 , 7 } βŠ‚ { 9 , 8 , π‘₯ } , find the value of π‘₯ .

Q6:

Given that { π‘₯ , 1 } βŠ‚ { 3 , 1 } , find the value of π‘₯ .

Q7:

Which of the following is true?

  • A β„€ βŠ‚ { βˆ’ 1 8 + | βˆ’ 2 0 | } βˆ’
  • B { βˆ’ 1 8 + | βˆ’ 2 0 | } βŠ‚ β„€ βˆ’
  • C { βˆ’ 1 8 + | βˆ’ 2 0 | } βŠ„ β„€ βˆ’

Q8:

Use βŠ‚ or βŠ„ to complete the following:  βˆ’ 1 7 4  β„€ + .

  • A βŠ„
  • B βŠ‚

Q9:

Pick the true statement.

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

Q10:

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

  • A 𝐴 βŠ‚ 𝐡 , 𝐴 βŠ„ 𝐢
  • B 𝐴 βŠ„ 𝐡 , 𝐴 βŠ‚ 𝐢
  • C 𝐴 βŠ„ 𝐡 , 𝐴 βŠ„ 𝐢
  • D 𝐴 βŠ‚ 𝐡 , 𝐴 βŠ‚ 𝐢

Q11:

If { 6 } βŠ„ { π‘₯ , 5 } , what are the possible values of π‘₯ ?

  • A6
  • B6 or 5
  • C π‘₯ can be any number other than 11.
  • D π‘₯ can be any number other than 6 or 5.
  • E π‘₯ can be any number other than 1.

Q12:

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

  • A βŠ‚
  • B βŠ„

Q13:

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

  • A βŠ‚
  • B βŠ„

Q14:

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

  • A βŠ„
  • B βŠ‚

Q15:

Given that { π‘₯ , 2 } βŠ‚ { 9 , 2 , 6 } and { 1 , π‘₯ , 4 } βŠ‚ { 1 , 6 , 4 , 3 } , find the value of π‘₯ .

  • A π‘₯ = 3
  • B π‘₯ = 9
  • C π‘₯ = 9 or π‘₯ = 6
  • D π‘₯ = 6
  • E π‘₯ = 6 or π‘₯ = 3

Q16:

Pick the true statement.

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

Q17:

Find all the subsets of 𝑋 = { π‘Ž , 𝑛 } .

  • A βˆ… , { π‘Ž } , { 𝑛 }
  • B { π‘Ž } , { 𝑛 } , { π‘Ž , 𝑛 }
  • C βˆ… , { π‘Ž 𝑛 } , { 𝑛 π‘Ž } , { π‘Ž , 𝑛 }
  • D βˆ… , { π‘Ž } , { 𝑛 } , { π‘Ž , 𝑛 }
  • E βˆ… , { π‘Ž } , { 𝑛 } , { π‘Ž 𝑛 } , { 𝑛 π‘Ž } , { π‘Ž , 𝑛 }

Q18:

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

  • A βŠ„
  • B βŠ‚

Q19:

Use βŠ‚ or βŠ„ to fill in the gap: If 𝐴 = { 5 , 3 , 1 , 6 } and 𝐡 = { 6 , 8 , 9 , 5 } , then 𝐡 𝐴 .

  • A βŠ„
  • B βŠ‚

Q20:

Given that { π‘₯ } βŠ‚ { 1 , 2 7 } , find the value of π‘₯ .

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

Q21:

Use βŠ‚ or βŠ„ to fill in the gap:

  • A βŠ„
  • B βŠ‚

Q22:

Find all the subsets of the set of the letters of ( ) y b b y .

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

Q23:

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

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

Q24:

Given that { π‘₯ , 3 } βŠ‚ { 1 1 , 5 , 𝑦 } , what are the possible values for π‘₯ and 𝑦 ?

  • A π‘₯ = 1 6 , 𝑦 = 3
  • B 𝑦 = 1 1 or 𝑦 = 5 , π‘₯ = 3
  • C π‘₯ = 6 , 𝑦 = 3
  • D π‘₯ = 1 1 or π‘₯ = 5 , 𝑦 = 3

Q25:

Find a subset of { 1 , 5 } .

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