Question

Which counterexample shows the conjecture “If the product of two numbers is positive, then the two numbers must both be positive” to be false?

(-3)(-1) = (+3)
(-3)(+1) = (-3)
(+3)(+1) = (+3)
(+3)(-1) = (-3)

Answer 1

(-3)(-1) = (+3)

Explanation:

The counterexample would be that the product of two negative numbers is positive but the numbers are negative. For example, (-3)(-1) = (+3).

Answer 2

(-3)(-1) = (+3)

Explanation:

In this question, we have to find the equation that proves the statement wrong.

The statement says that “If the product of two numbers is positive, then the two numbers must both be positive"

We can already make this statement false because both numbers doesn't only have to be positive in order to have the product of a positive number.

We know that if you multiply two negatives, the number turns positive.

Therefore, we can see that displayed in this equation: (-3)(-1) = (+3)

This is because (-3)(-1) = 3, and they both aren't positive numbers.