Math Problem Statement

  1. Bonus: Give a second, different definition of B using set-builder notation. B = {0, 2, 4, 6, 8}

Solution

To provide a second definition of the set B={0,2,4,6,8}B = \{0, 2, 4, 6, 8\} using set-builder notation, we can describe the elements of BB in a different way. One approach is to describe BB as the set of all non-negative even integers less than 10.

Here’s a different definition using set-builder notation:

B={xZ0x<10 and x is even}.B = \{ x \in \mathbb{Z} \mid 0 \leq x < 10 \text{ and } x \text{ is even} \}.

Explanation:

  • xZx \in \mathbb{Z} specifies that xx is an integer.
  • 0x<100 \leq x < 10 restricts xx to be between 0 and 9, inclusive.
  • xx is even ensures that xx is an even number, which gives us the set {0,2,4,6,8}\{0, 2, 4, 6, 8\}.

Would you like more details or have any questions about this?

Here are 5 related questions to expand on this topic:

  1. What is the set-builder notation for the set of all odd integers less than 10?
  2. How would you represent the set {1,3,5,7,9}\{1, 3, 5, 7, 9\} using a rule for odd numbers in set-builder notation?
  3. What are some other ways to describe the set of all non-negative integers less than 10?
  4. How can set-builder notation be used to describe infinite sets?
  5. What is the difference between describing a set using set-builder notation versus listing its elements?

Tip: When using set-builder notation, always ensure that the conditions clearly and uniquely define each element of the set.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Set-builder Notation

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12