Set Builder Notation Mastery
This worksheet helps Grade 12 students master set builder notation, including defining sets, understanding properties, and converting between roster and set builder forms.
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Set Builder Notation Mastery
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Read each question carefully and provide your answer in the space provided. Show all necessary work for full credit.
1. Define the following sets using set-builder notation:
a) The set of all even integers.
b) The set of all real numbers greater than 5.
c) The set of all prime numbers less than 20.
2. Write the following sets in roster form:
a) A = {x | x ∈ ℤ, -3 < x ≤ 2} A =
b) B = {y | y ∈ ℝ, y² = 9} B =
c) C = {n | n is a natural number and n is a multiple of 3, n < 15} C =
3. Which of the following statements is TRUE for the set A = {x | x is an integer, x > 0 and x < 5}?
A = {1, 2, 3, 4, 5}
A contains negative numbers.
A is an infinite set.
A = {1, 2, 3, 4}
4. Determine whether each statement is True or False.
a) The set {x | x is a letter in the word 'mathematics'} is equal to the set {m, a, t, h, e, i, c, s}.
True
False
b) The empty set can be represented as {0}.
True
False
5. Express the following intervals using set-builder notation:
a) (-∞, 7]
b) [2, 10)
6. Consider the set D = {x | x ∈ ℤ, x² < 25}. Write set D in roster form.