Find one counterexample to show that each conjecture is false.

The product of two positive numbers is greater than either number.

the sum of two numbers is greater than either number

2 &2

Find one counterexample:

"The product of two positive numbers is greater than either number"

For example: 5*(1/2)=2.5 < 5

If at least one of the numbers is smaller than one, then the product is smaller than at least one of the two numbers. For example:
5*(1/2)=2.5 < 5

Sure, here's a counterexample to show that the conjecture is false: Suppose we have the positive numbers 2 and 3. When we multiply these numbers together (2 * 3), we get the result of 6. However, 6 is not greater than either 2 or 3, so this counterexample proves that the conjecture is false.

To find a counterexample for this conjecture, we need to provide an example where the product of two positive numbers is not greater than either number.

Let's consider the positive numbers 2 and 3. According to the conjecture, the product of these two numbers should be greater than either of them. However, the product of 2 and 3 is 6, which is not greater than 2 or 3.

Therefore, the example 2 and 3 serves as a counterexample to this conjecture, showing that it is false.