Worksheet: Expressing a Set

In this worksheet, we will practice expressing a set by identifying its elements.

Q1:

Using the listing method, express the set of the days of the week.

  • A{Sunday, Monday, Tuesday, Wednesday}
  • B{Saturday, Sunday, Monday, Tuesday, Wednesday, Thursday}
  • C{Saturday, Sunday, Monday, Tuesday, Wednesday, Thursday, Friday}
  • D{Sunday, Monday, Tuesday, Wednesday, Thursday}
  • E{Sunday, Monday, Tuesday}

Q2:

Using the listing method, write the set of months of the year that begin with the letter “A”.

  • A{August}
  • B{January, February, March, May}
  • C{April, August}
  • D{April, August, January, February, March, May}
  • E{Autumn}

Q3:

𝑋 is the set of odd numbers greater than 2 and less than 10. Write 𝑋 using the listing method.

  • A𝑋={3,5,7,9}
  • B𝑋={2,3,5,7,9,10}
  • C𝑋={4,6,8}
  • D𝑋={3,5,7,9,10}
  • E𝑋={2,3,5,7,9}

Q4:

Find the set of natural numbers that are less than 7.

  • A{0,1,2,3,4,5,6,7}
  • B{1,2,3,4,5,6}
  • C{0,2,4,6}
  • D{0,1,2,3,4,5,6}

Q5:

𝑋 is the set of odd numbers greater than 8. Write 𝑋 using the listing method.

  • A𝑋={11,13,15,}
  • B𝑋={10,12,14,}
  • C𝑋={8,9,11,}
  • D𝑋={9,11,13,}

Q6:

Given that 𝑋={𝑥𝑥,𝑥5}, write 𝑋 using the listing method.

  • A𝑋={5,6,7,}
  • B𝑋={6,7,8,}
  • C𝑋={4,3,2,}
  • D𝑋={5,4,3,}

Q7:

Given that 𝑋={𝑥𝑥,18𝑥<14}, write 𝑋 using the listing method.

  • A𝑋={18,17,16,15}
  • B𝑋={17,16,15,14}
  • C𝑋={17,16,15}
  • D𝑋={18,17,16,15,14}

Q8:

𝐴 is the set of whole numbers a such that 7>𝑎. Write 𝐴 using the listing method.

  • A𝐴={8,9,10,}
  • B𝐴={0,1,2,3,4,5,6}
  • C𝐴={0,1,2,3,4,5,6,7}
  • D𝐴={7,8,9,10,}

Q9:

Using the listing method, write the set of integers that are greater than 155.

  • A{153,151,149,147,145,}
  • B{156,157,158,159,160,}
  • C{155,154,153,152,151,}
  • D{155,156,157,158,159,}
  • E{154,153,152,151,150,}

Q10:

𝑌 is the set of digits in the number 90,590. Write 𝑌 using the listing method.

  • A𝑌={9,0,5,9,0}
  • B𝑌={9,5,0}
  • C𝑌={90,590}
  • D𝑌={90,5,90}

Q11:

𝑀 is the set of all two-digit numbers which are divisible by 22. Write 𝑀 using the listing method.

  • A𝑀={22,44,66,88}
  • B𝑀={22,44,66,88,110}
  • C𝑀={22,44,66}
  • D𝑀={44,66,88}

Q12:

𝑌 is the set of prime numbers greater than 7 and less than 25. Write 𝑌 using the listing method.

  • A𝑌={13,17,19,23}
  • B𝑌={11,13,17,19,23}
  • C𝑌={9,11,13,15,17,19,21,23}
  • D𝑌={11,13,17,19}

Q13:

𝐴={304,306,308}. Which statement describes 𝐴?

  • A𝐴 is the set of odd numbers between 303 and 309
  • B𝐴 is the set of prime numbers between 303 and 309
  • C𝐴 is the set of even numbers between 303 and 309
  • D𝐴 is the set of the whole numbers between 303 and 309

Q14:

Write the elements of the set: The whole numbers between (but not including) 35 and 41.

  • A34, 36, 37, 38, 39, 40
  • B36, 37, 38, 39, 40
  • C37, 38, 39, 40, 42
  • D36, 38, 39, 40

Q15:

Find all the elements of the set of 2-digit numbers whose 2 digits are the same.

  • A12, 21, 23, 32, 45, 54, 78, 87, 99
  • B11, 22, 33, 44, 55, 66, 77, 88, 99
  • C11, 22, 33, 55, 66, 77, 88, 99
  • D12, 21, 24, 42, 67, 76, 79, 97

Q16:

Write the elements of the set: Theprimefactorsof35.

  • A1,5,7
  • B6,8
  • C4,6
  • D5,7

Q17:

Write the elements of the set: The even numbers between (but not including) 59 and 63.

  • A60 , 62, 64
  • B60, 62
  • C58 , 60, 62
  • D61, 62

Q18:

Write the elements of the set: The 2-digit numbers that have 7 in the units position.

  • A17,27,37,47,57,67,77,87,97
  • B17,27,37,47,57,67,77,87
  • C27,37,47,57,67,77,87,97
  • D17,27,37,47,57,68,77,87,97

Q19:

Write the elements of the set:

The odd numbers between, but not including, 799 and 805.

  • A801, 803
  • B797, 802, 804
  • C801, 805
  • D799, 801, 803

Q20:

𝑋 is the set of even numbers greater than 4 and less than 8. Write 𝑋 using the listing method.

  • A𝑋={6}
  • B𝑋={4,6,8}
  • C𝑋={5,7}
  • D𝑋={6,8}
  • E𝑋={4,6}

Q21:

Given that 𝑋={𝑥𝑥,𝑥<1}, write 𝑋 using the listing method.

  • A𝑋={1,2,3,}
  • B𝑋={0,1,2,}
  • C𝑋={1,0,1,}
  • D𝑋={2,3,4,}

Q22:

Given that 𝑋={𝑥𝑥,3<𝑥<7}, write 𝑋 using the listing method.

  • A𝑋={4,5,6}
  • B𝑋={4,5,6,7}
  • C𝑋={3,4,5,6}
  • D𝑋={3,4,5,6,7}

Q23:

Given that 𝑋={𝑥𝑥,15𝑥<10}, write 𝑋 using the listing method.

  • A𝑋={15,14,13,12,11}
  • B𝑋={14,13,12,11,10}
  • C𝑋={14,13,12,11}
  • D𝑋={15,14,13,12,11,10}

Q24:

Using the listing method, write the set of integers that are greater than 46.

  • A{48,50,52,54,56,}
  • B{45,44,43,42,41,}
  • C{46,47,48,49,50,}
  • D{46,45,44,43,42,}
  • E{47,48,49,50,51,}

Q25:

How many elements does 𝑋={43,20,40,12,31} have?

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