Math Problem Statement

Express the following set in​ set-builder notation. B = {14, 15, 16, 17, 18, 19, 20, 21}

Solution

The set B={14,15,16,17,18,19,20,21}B = \{ 14, 15, 16, 17, 18, 19, 20, 21 \} consists of consecutive integers starting from 14 to 21.

We can express this set in set-builder notation as:

B={xxZ,14x21}B = \{ x \mid x \in \mathbb{Z}, 14 \leq x \leq 21 \}

Where:

  • xx is the element of the set.
  • Z\mathbb{Z} represents the set of integers.
  • The condition 14x2114 \leq x \leq 21 specifies that xx is an integer between 14 and 21 (inclusive).

Let me know if you'd like further clarification or have any questions!

Related questions:

  1. How can we express a set of even numbers between 10 and 30 in set-builder notation?
  2. What is the difference between set-builder notation and roster notation?
  3. How would you represent the set of all prime numbers less than 50 in set-builder notation?
  4. How would you describe the set of all real numbers greater than 5 but less than 10?
  5. What are some examples of using set-builder notation for describing geometric shapes like circles or squares?

Tip:

When using set-builder notation, always make sure to clearly define the properties or conditions that an element must satisfy to belong to the set.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Set-Builder Notation
Integers

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9