Which value of m is a counterexample for the following statement?If m is an odd prime number, then m + 2 is also prime.
Question
Which value of m is a counterexample for the following statement?
If m is an odd prime number, then m + 2 is also prime.
Solution
A counterexample for the statement "If m is an odd prime number, then m + 2 is also prime" is m = 7.
Here's the step-by-step explanation:
- Start with the given statement: "If m is an odd prime number, then m + 2 is also prime."
- We need to find an odd prime number such that when we add 2 to it, the result is not a prime number.
- Let's try m = 7, which is an odd prime number.
- Add 2 to m: 7 + 2 = 9.
- Check if 9 is a prime number. A prime number is a number that has exactly two distinct positive divisors: 1 and itself. The number 9 has divisors 1, 3, and 9. Therefore, 9 is not a prime number.
- So, m = 7 is a counterexample for the given statement.
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