Let P(x) denote “x ≤ 1” and U be the set of natural numbers. Which of the following values of x is true? a. 0 b. 0.5 c. square root of 1 d. 4/2

Given that \( P(x) \) represents the statement "x ≤ 1" and \( U \) is the set of natural numbers, we need to determine which of the provided values of \( x \) makes \( P(x) \) true.

### Consider the following:

1. **Option a: \( x = 0 \)**
   - \( 0 \leq 1 \) is true.
   - \( 0 \) is a natural number.
   - **Conclusion: True**

2. **Option b: \( x = 0.5 \)**
   - \( 0.5 \leq 1 \) is true.
   - However, \( 0.5 \) is not a natural number.
   - **Conclusion: False**

3. **Option c: \( x = \sqrt{1} \)**
   - \( \sqrt{1} = 1 \), so \( 1 \leq 1 \) is true.
   - \( 1 \) is a natural number.
   - **Conclusion: True**

4. **Option d: \( x = \frac{4}{2} \)**
   - \( \frac{4}{2} = 2 \), but \( 2 \leq 1 \) is false.
   - **Conclusion: False**

### Answer:
The values of \( x \) that make \( P(x) \) true are:
- **a. 0**
- **c. \( \sqrt{1} \)**

Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. What is the definition of natural numbers?
2. Can \( P(x) \) include irrational numbers under a different set of conditions?
3. How would the answer change if \( P(x) \) represented \( x \geq 1 \)?
4. What are the properties of square roots with respect to inequalities?
5. How do rational numbers differ from natural numbers in such inequality problems?

**Tip:** When solving inequalities, always consider the type of numbers involved (e.g., natural, rational, irrational) to avoid incorrect conclusions.

Explore how to solve the inequality P(x) ≤ 1 within the set of natural numbers. Understand key mathematical concepts such as inequalities, square roots, and set theory. This problem provides a detailed solution suitable for students in Grades 6-8.

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