Understanding Sets: Roster and Set Builder Notation

This video tutorial covers the basics of set notation, including roster and set builder methods. It explains how to represent different types of numbers, such as natural, whole, integers, even, odd, prime, and perfect square numbers, using these notations. The tutorial provides step-by-step examples to help learners understand how to define and describe sets of numbers effectively.

Which of the following is a correct representation of natural numbers less than 6 in roster notation?

• {0, 1, 2, 3, 4}

• {1, 2, 3, 4, 5, 6}

• {1, 2, 3, 4, 5}

• {0, 1, 2, 3, 4, 5}

How would you express the set of whole numbers less than 8 using set builder notation?

• {x | x is a whole number, 0 ≤ x < 8}

• {x | x is a whole number, 1 ≤ x ≤ 7}

• {x | x is a whole number, 0 < x ≤ 8}

• {x | x is a whole number, 1 ≤ x < 8}

What is the correct roster notation for integers greater than -4 and less than or equal to 5?

• {-3, -2, -1, 0, 1, 2, 3, 4}

• {-2, -1, 0, 1, 2, 3, 4, 5}

• {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5}

• {-3, -2, -1, 0, 1, 2, 3, 4, 5}

Which set builder notation correctly describes the set of positive even numbers less than 15?

• {x | x is an even number, 1 ≤ x < 15}

• {x | x is an even number, 2 ≤ x < 15}

• {x | x is a positive even number, 2 ≤ x < 15}

• {x | x is a positive even number, 1 ≤ x ≤ 7}

Identify the correct roster notation for odd numbers greater than or equal to -7 and less than 5.

• {-7, -5, -3, -1, 1, 3}

• {-5, -3, -1, 1, 3, 5}

• {-7, -5, -3, -1, 1, 3, 5}

• {-6, -4, -2, 0, 2, 4}

Which of the following is a prime number less than 12?

• 11

• 9

• 6

• 4

What is the correct set builder notation for the set of positive prime numbers less than 12?

• {x | x is a prime number, 1 < x < 12}

• {x | x is a prime number, 2 ≤ x < 12}

• {x | x is a prime number, 1 ≤ x ≤ 11}

• {x | x is a prime number, 2 ≤ x ≤ 11}

Which of the following numbers is a perfect square less than 120?

• 121

• 144

• 130

• 100

How would you express the set of positive perfect square numbers less than 120 using set builder notation?

• {x^2 | x is a natural number, 1 ≤ x ≤ 10}

• {x^2 | x is a natural number, 0 < x < 11}

• {x^2 | x is a natural number, 0 ≤ x ≤ 10}

• {x^2 | x is a natural number, 1 ≤ x < 11}

Which of the following is not a perfect square?

• 16

• 49

• 25

• 30