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 .

  • A equivalent
  • B not equal
  • C not equivalent
  • D equal

Q2:

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

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

Q3:

Given that { 0 , 4 , 𝑎 } = { 4 , 1 2 , 𝑏 } = { 0 , 1 2 , 𝑐 } , find 𝑎 , 𝑏 , and 𝑐 .

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

Q4:

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

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

Q5:

Use = or to fill in the blank:

  • A
  • B =

Q6:

Use = or to fill in the blank: { 1 , 2 , 1 9 , 3 8 } 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 { 4 𝑥 } = { 2 8 } .

Q10:

Use = or to fill in the blank: If 𝑥 = 0 , then { 𝑥 , 2 , 1 6 } { 2 , 1 6 , 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: { 2 8 } the set of even numbers smaller than 28.

  • A
  • B =

Q13:

If { 6 3 , 𝑏 } = { 𝑐 , 6 3 } , what are the possible values of 𝑏 and 𝑐 ?

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

Q14:

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

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

Q15:

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

  • AYes
  • BNo

Q16:

Given that { 𝑏 , 8 } = { 𝑐 , 1 } , find 𝑏 and 𝑐 .

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

Q17:

Given that 𝐴 = { 5 , 7 , 8 } and 𝐶 = { 𝑥 𝑥 is a digit in the number 5 7 7 8 5 } , 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 = 8 , 𝑐 = 3
  • B 𝑏 = 9 , 𝑐 = 3
  • C 𝑏 = 3 , 𝑐 = 8
  • D 𝑏 = 3 , 𝑐 = 9
  • E 𝑏 = 3 , 𝑐 = 1 2

Q19:

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

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