Worksheet: Equal Sets

In this worksheet, we will practice identifying equal sets and using their equality to find the value of unknown elements.

Q1:

If two sets have the exact same elements, they are said to be .

  • Aequivalent
  • Bnot equal
  • Cequal
  • Dnot equivalent

Q2:

Given that {𝑏,3,4}={𝑐,9,4}, find 𝑏 and 𝑐.

  • A 𝑏 = 9 , 𝑐 = 4
  • B 𝑏 = 9 , 𝑐 = 1 2
  • C 𝑏 = 4 , 𝑐 = 9
  • D 𝑏 = 9 , 𝑐 = 3
  • E 𝑏 = 3 , 𝑐 = 9

Q3:

Given that {0,4,𝑎}={4,12,𝑏}={0,12,𝑐}, find 𝑎, 𝑏, and 𝑐.

  • A 𝑎 = 1 2 , 𝑏 = 4 , 𝑐 = 0
  • B 𝑎 = 4 , 𝑏 = 0 , 𝑐 = 1 2
  • C 𝑎 = 0 , 𝑏 = 1 2 , 𝑐 = 4
  • D 𝑎 = 1 2 , 𝑏 = 0 , 𝑐 = 4

Q4:

If {4𝑏}{44}, what are the possible values of 𝑏?

  • A 𝑏 can be any number except 0 and 11.
  • B 𝑏 can be any number except 44.
  • C 𝑏 can be any number except 4 and 44.
  • D 𝑏 can be any number except 11.

Q5:

Use = or to fill in the blank: {2,8,6}{28,6}.

  • A =
  • B

Q6:

Use = or to fill in the blank: {1,2,19,38} the set of factors of the number 38.

  • A =
  • B

Q7:

Two equal sets are equivalent. Are two equivalent sets equal?

  • Ano
  • Byes

Q8:

If {3,5,1}={1,3,𝑥}, what is the value of 𝑥?

Q9:

Find the value of 𝑥 if {4𝑥}={28}.

Q10:

Use = or to fill in the blank: If 𝑥=0, then {𝑥,2,16}{2,16,1}.

  • A
  • B =

Q11:

Use = or to fill in the blank: {4,9,8} the set of digits of the number 4,998.

  • A
  • B =

Q12:

Use = or to fill in the blank: {28} the set of even numbers smaller than 28.

  • A
  • B =

Q13:

If {63,𝑏}={𝑐,63}, what are the possible values of 𝑏 and 𝑐?

  • A 𝑏 and 𝑐 can be any number except 0 and 1.
  • B 𝑏 and 𝑐 can be any number except 0 and 63.
  • C 𝑏 and 𝑐 can be any number except 63.
  • D 𝑏 and 𝑐 can be any number except 1.

Q14:

Use = or to fill in the blanks: If 𝑋={0,3}, 𝑌 is the set of digits of 30, and 𝑍={30}, then 𝑋𝑌 and 𝑌𝑍.

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

Q15:

Are these two sets equivalent?𝑋={2,3,9}𝑌={2,9,3}and.

  • AYes
  • BNo

Q16:

Given that {𝑏,8}={𝑐,1}, find 𝑏 and 𝑐.

  • A 𝑏 = 7 , 𝑐 = 9
  • B 𝑏 = 9 , 𝑐 = 7
  • C 𝑏 = 1 , 𝑐 = 8
  • D 𝑏 = 8 , 𝑐 = 1
  • E 𝑏 = 1 , 𝑐 = 9

Q17:

Given that 𝐴={5,7,8} and 𝐶={𝑥𝑥 is a digit in the number 57,785}, find the relation between 𝐴 and 𝐶.

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

Q18:

Given that {9,𝑏,8}={3,𝑐,8}, find 𝑏 and 𝑐.

  • A 𝑏 = 3 , 𝑐 = 8
  • B 𝑏 = 3 , 𝑐 = 1 2
  • C 𝑏 = 8 , 𝑐 = 3
  • D 𝑏 = 3 , 𝑐 = 9
  • E 𝑏 = 9 , 𝑐 = 3

Q19:

If {𝑥,9,1}={1,3,9}, what is the value of 𝑥?

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