Set Builder Notation Concepts

This lesson introduces set builder notation, a method to describe sets, especially useful for infinite sets. It covers how to read and write set builder notation, compares it to other methods, and provides examples. The lesson also explains graphing intervals using set builder notation and inequalities, including compound inequalities. Finally, it demonstrates set builder notation with even numbers and concludes with a summary.

What is the primary purpose of set builder notation?

• To list all elements of a set explicitly

• To describe a set using a rule or condition

• To graph a set on a number line

• To compare different sets

Which of the following is a correct representation of set builder notation?

• (x ; x > 0)

• {x ; x > 0}

• {x | x > 0}

• [x : x > 0]

In set builder notation, what does the vertical bar or colon represent?

• The beginning of the set

• The end of the set

• A condition or restriction

• A list of elements

How is the interval from -2 to 3, including 3, represented in set builder notation?

• {x | x < 3}

• {x | x ≥ -2}

• {x | x ≤ 3}

• {x | x > -2}

What does a closed point on a number line indicate?

• The interval is finite

• The interval is infinite

• The number is included in the interval

• The number is not included in the interval

How would you express the interval -2 < x ≤ 6 using set builder notation?

• {x | x ≥ -2 and x < 6}

• {x | x ≤ -2 and x > 6}

• {x | x < -2 and x ≥ 6}

• {x | x > -2 and x ≤ 6}

What is the interval notation for the set of all x such that x > -2?

• (-∞, -2)

• [-2, ∞)

• (-2, 0)

• (-2, ∞)

Which set is represented by the set builder notation {x | x = 2n, n ∈ Z}?

• The set of all odd numbers

• The set of all even numbers

• The set of all prime numbers

• The set of all integers

What does the capital 'Z' represent in set builder notation?

• The set of real numbers

• The set of rational numbers

• The set of natural numbers

• The set of integers

What is the significance of using set builder notation over basic inequality notation?

• It is easier to understand

• It is more formal

• It is less precise

• It is less formal