We are given two sets \( P \) and \( N \):

- \( P = \{ y \mid y < 0 \} \) (The set of all values less than 0)
- \( N = \{ y \mid y \geq 5 \} \) (The set of all values greater than or equal to 5)

Now, we are asked to find the union of these two sets, denoted as \( N \cup P \).

The union of two sets includes all elements that are in either one of the sets or in both. Therefore, the union of \( N \) and \( P \) is the set of all values that are either less than 0 (from \( P \)) or greater than or equal to 5 (from \( N \)).

Thus, the union is:
\[
N \cup P = \{ y \mid y < 0 \text{ or } y \geq 5 \}
\]

### Final Answer:
\[
N \cup P = (-\infty, 0) \cup [5, \infty)
\]

Would you like more details, or do you have any questions?

Here are some related questions:

1. What would the intersection \( N \cap P \) be?
2. What is the difference between \( N \) and \( P \)?
3. How would this change if \( N = \{ y \mid y > 3 \} \)?
4. Can you visualize the sets on a number line?
5. What are the properties of set unions?

**Tip:** In interval notation, square brackets \([ \, ]\) denote closed intervals, while parentheses \(( \, )\) denote open intervals.

P = { y | y < 0 } N = { y | y >= 5 } N U P

Learn how to find the union of two sets, P = { y | y < 0 } and N = { y | y >= 5 }, using set theory and interval notation. This problem covers key concepts like inequalities and union operations, suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation