Math Problem Statement

Write the set of points from −5 to −1 but excluding −2 and −1 as a union of intervals:

Solution

The set of points from 5-5 to 1-1 but excluding 2-2 and 1-1 can be written as the following union of intervals:

[5,2)(2,1)[-5, -2) \cup (-2, -1)

This represents the interval from 5-5 to 2-2 (excluding 2-2), and the interval from just after 2-2 to 1-1 (excluding 1-1).

Would you like any more details or have any questions?

Here are 5 related questions to explore further:

  1. How do you represent the union of intervals graphically on a number line?
  2. What is the difference between open and closed intervals?
  3. How would the interval notation change if 2-2 were included?
  4. What is the difference between union and intersection of intervals?
  5. How can set-builder notation be used to represent the same set?

Tip: When working with intervals, remember that square brackets [][ \, ] indicate that the endpoints are included (closed interval), while parentheses ()( \, ) indicate that the endpoints are not included (open interval).

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Math Problem Analysis

Mathematical Concepts

Intervals
Set Theory

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12