Question

Show the following conjectures are false by finding a counterexample.

13. All prime numbers are odd.

14. If the product of two numbers is positive, then the two numbers must both be positive.

15. If the sidewalk is wet, then it has been raining.

Answer 1

''All prime numbers are odd."

That is incorrect because if we consider the smallest odd number, 2, is an even number. We can say that except 2, all prime numbers are odd.

14. section is wrong. For example, both numbers can be negative, so when we multiple these two, it will equals a positive value.