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:
- What is a converse in mathematical logic?
- Can the contrapositive of a statement be false as well?
- Are all prime numbers odd, or are there exceptions?
- Can a statement and its converse both be true?
- 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