Math Problem Statement

Choose the correct Roster Form for the set written in Set-builder form: {x : x is an integer and x > 2}.

Solution

The question asks for the roster form of the set defined in set-builder notation:

{x:x is an integer and x>2}\{ x : x \text{ is an integer and } x > 2 \}

In set-builder notation, this defines the set of all integers greater than 2.

Solution:

To translate this into roster form, list the elements of the set that satisfy the condition x>2x > 2:

  • Starting from the smallest integer greater than 2, the set would include 3,4,5,6,3, 4, 5, 6, \dots.

The correct roster form of the set is: {3,4,5,6,}\{3, 4, 5, 6, \dots\}

Answer:

The correct answer is:

  • Option 1: {3,4,5,6,}\{3, 4, 5, 6, \dots\}

Would you like further explanation, or do you have any questions about subsets or set notation?

Related Questions:

  1. What is the difference between roster form and set-builder form?
  2. How do you represent sets of negative integers in set-builder notation?
  3. What is the roster form of {x:x is an integer and x5}\{ x : x \text{ is an integer and } x \leq 5 \}?
  4. How would you write {3,4,5,6,}\{3, 4, 5, 6, \dots\} in set-builder notation for different conditions?
  5. Can set-builder form be used for non-integer sets, like all real numbers greater than 2?

Tip:

In set-builder notation, always look carefully at the conditions given to determine the range or type of elements in the set.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Roster Form
Set-builder Notation

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9