Math Problem Statement

Find a counterexample that demonstrates that the converse of If you chose number 13, then you chose a prime number Is false

Solution

The original statement is:

"If you chose number 13, then you chose a prime number."

This statement is true because 13 is indeed a prime number.

Now, we are tasked with finding a counterexample that shows the converse is false. The converse of the original statement is:

"If you chose a prime number, then you chose number 13."

To show this is false, we need a prime number that is not 13. Any such number will serve as a counterexample.

A counterexample is:

2.

Explanation:

  • 2 is a prime number.
  • But if you chose 2, you did not choose 13, which proves the converse is false.

Would you like more details or have any other questions?

Here are 5 questions to expand on this:

  1. What is a converse in mathematical logic?
  2. Can the contrapositive of a statement be false as well?
  3. Are all prime numbers odd, or are there exceptions?
  4. Can a statement and its converse both be true?
  5. How do you prove a statement is true for all cases?

Tip: In logic, the truth of a statement does not guarantee the truth of its converse. Always check them separately.

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Math Problem Analysis

Mathematical Concepts

Logic
Prime Numbers

Formulas

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Theorems

Converse of a Statement

Suitable Grade Level

Grades 8-10