Question

Select a counter-example that makes the conclusion false.

7 - 3 = 4, 8 - 5 = 3, 9 - 8 = 1

Conclusion: the difference of two positive numbers is always positive.

Counterexample:

Answer 1

while none of these examples can be used as an counterexample i could make one up to prove the conclusion is false.   ex: 3-5=-2

Answer 2

It is not necessary that the difference of two positive number is always positive.

Explanation:

We are given the following conclusion:

The difference between two positive number is always positive.

We have to provide a counter example to show that this conclusion is false.

It is not necessary that the difference is always positive.

The given examples are :

7 -3 = 4

8 - 5 = 3

9 - 8 = 1

The counter examples can be of the form:

3 - 7 = -4

5 - 8 = -3

8 - 9 = -1

2 - 8 = -6

Thus, we can always find a pair of positive numbers whose difference is negative.