Math Problem Statement

Use the following roster notations to write in set builder notation, use x as the variable: {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36}.

Solution

It looks like this is the same image from earlier, showing the same problem on set builder notation for the set of even integers:

{2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36}\{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36\}

To fill in the blanks based on the instructions:

  • You are asked to express the set using set-builder notation with xx as the variable.

Here is how you would complete it:

  1. Select "even" from the dropdown, as the set contains even integers.
  2. The range is between 2 and 36, so you would fill in the numbers 2 and 36 in the respective blanks.

The full set-builder notation would look like this:

{xx is an even integer between 2 and 36}\{ x \mid x \text{ is an even integer between } 2 \text{ and } 36 \}

Ensure you select "even" from the dropdown menu as it matches the pattern of the set.

Do you have any further questions or need clarification?

Here are five related questions:

  1. How would you express the set of multiples of 5 between 5 and 50 in set-builder notation?
  2. If the set contained all odd integers from 1 to 21, how would the set-builder notation change?
  3. What is the difference between expressing a finite set and an infinite set in set-builder notation?
  4. How would you handle a set that includes both even and odd numbers but with specific intervals, like {1,4,7,10}\{1, 4, 7, 10\}?
  5. What is the importance of set-builder notation in defining sets with more complex conditions, such as inequalities?

Tip: When converting a set to set-builder notation, focus on identifying patterns such as "even", "odd", or "multiples" to describe the set concisely.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Set Builder Notation
Even Numbers

Formulas

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Theorems

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Suitable Grade Level

College Level (Algebra)