https://file.aiquickdraw.com/mathbot/file/17256755098255olnknqe.jpg

The image shows a question about logical statements related to a conditional statement: **"If a number is a natural number, then it is also a whole number."**

Let’s analyze the key concepts and write out the needed statements (Inverse, Converse, Contrapositive, Bi-Conditional) along with their truth values.

1. **Conditional statement (Given):**  
   "If a number is a natural number, then it is also a whole number."
   - Natural numbers are {1, 2, 3, ...}, and whole numbers are {0, 1, 2, 3, ...}.
   - Truth Value: **True** (because every natural number is also a whole number).

### 1. Inverse:  
   The inverse negates both parts of the original statement:  
   - "If a number is not a natural number, then it is not a whole number."
   - **Truth Value:** **False** (because numbers like 0 are whole but not natural).

### 2. Converse:  
   The converse switches the hypothesis and conclusion of the original statement:  
   - "If a number is a whole number, then it is a natural number."
   - **Truth Value:** **False** (because 0 is a whole number but not a natural number).

### 3. Contrapositive:  
   The contrapositive negates and switches the hypothesis and conclusion:  
   - "If a number is not a whole number, then it is not a natural number."
   - **Truth Value:** **True** (since any number that is not whole cannot be natural).

### 4. Bi-Conditional:  
   The bi-conditional requires both directions (the original statement and its converse) to be true:  
   - "A number is a natural number if and only if it is a whole number."
   - **Truth Value:** **False** (since 0 is a whole number but not a natural number).

---

### Summary:
- **Inverse (16):** If a number is not a natural number, then it is not a whole number.  
   **Truth Value (17):** False.
- **Converse (18):** If a number is a whole number, then it is a natural number.  
   **Truth Value (19):** False.
- **Contrapositive (20):** If a number is not a whole number, then it is not a natural number.  
   **Truth Value (21):** True.
- **Bi-Conditional (22):** A number is a natural number if and only if it is a whole number.  
   **Truth Value (23):** False.

Let me know if you need further clarifications or details!

---

### Relative questions to explore:
1. What is the difference between natural and whole numbers?
2. How would the statements change if 0 were considered a natural number?
3. Can you explain the truth values for other conditional statements?
4. What are some real-world examples of bi-conditional statements?
5. How is the contrapositive logically equivalent to the original statement?

### Tip:  
When negating mathematical statements, be careful with definitions (e.g., natural vs whole numbers) to ensure accurate truth values.

If a number is a natural number, then it is also a whole number.

Explore the logical analysis of the statement 'If a number is a natural number, then it is also a whole number.' Learn about the inverse, converse, contrapositive, and bi-conditional statements with truth values. This problem is suitable for high school students studying logical reasoning.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation