Question

Prove that if p is a prime number and r is an integer with 0
a) True
b) False

Answer 1

The statement is False because there exists a counterexample.

Step-by-step explanation:

The statement is b) False.

To prove this, we need to show a counterexample where p is a prime number and r is an integer, and the statement doesn't hold true. Let's take p = 2 and r = 4. Here, A represents the event that p is a prime number, and B represents the event that r is an integer with 0 < r < p. In this case, A is true because 2 is a prime number, and B is also true because 0 < 4 < 2. However, the statement P(A AND B) = 0 is false because the intersection of A and B is not empty. Therefore, the statement is false.