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The given conditional statement is:

**"If a number is not a real number, then it is not a rational number."**

To find the contrapositive of this conditional statement:

1. First, negate both parts of the statement.
2. Then, switch the two parts.

### Original Statement:
- Hypothesis (P): A number is not a real number.
- Conclusion (Q): The number is not a rational number.

### Contrapositive:
- Negate both P and Q.
  - Negation of "A number is not a real number" is "A number is a real number."
  - Negation of "The number is not a rational number" is "The number is a rational number."

- Swap the two:
  - "If a number is a rational number, then it is a real number."

This is the contrapositive: **"If a number is a rational number, then it is a real number."**

### Is the Contrapositive True or False?

This contrapositive is **true**, because all rational numbers are real numbers by definition. A rational number can be expressed as a fraction, and all rational numbers fall under the set of real numbers.

Thus, the correct answer is:

**The contrapositive of the statement is true.**

Would you like further details or explanations?

Here are 5 related questions to explore further:

1. What is the converse of the given statement, and is it true?
2. Can you give an example of a real number that is not rational?
3. What is the inverse of this conditional statement, and is it true?
4. How do contrapositive statements relate to logical equivalence?
5. Can a number be irrational but still real?

**Tip:** The contrapositive of a true statement is always true.

If a number is not a real number, then it is not a rational number. Determine the contrapositive of the statement and whether it is true or false.

Learn how to determine the contrapositive of the conditional statement 'If a number is not real, it is not rational' and verify whether it is true or false. This concept applies to logic and mathematical reasoning, suitable for high school students.

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