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.