No, the interval \((- \infty, 2) \cup (2, 5)\) does not include 2.

In interval notation:
- \((- \infty, 2)\) means all real numbers less than 2 but **not** including 2.
- \((2, 5)\) means all real numbers greater than 2 but **not** including 2.

Since 2 is not included in either interval, it is excluded from the union.

Would you like further clarification or details? Here are five related questions to explore:

1. How do we determine whether a number is included in an interval?
2. What is the difference between open and closed intervals?
3. How does interval notation represent infinite sets?
4. Can the union of two intervals ever include a boundary point if one interval excludes it?
5. How would the set change if the intervals were closed at 2?

**Tip:** In interval notation, parentheses \(()\) represent open intervals (excluding the endpoints), while square brackets \([]\) represent closed intervals (including the endpoints).

Does (-infinity,2) union (2,5) include 2?

Explore whether the union of intervals (-∞, 2) and (2, 5) includes the number 2. This problem covers key concepts in set theory, interval notation, and the properties of open intervals. Ideal for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation