Question

- Find a counterexample to show that the conjecture is false The sum of a positive number and a negative number is always positive.

Answer 1

The sum of a positive number and a negative number is always positive.

So:

Let:

a = arbitrary number where a>0

b = another arbitrary number where b<0

According to the conjecture:

a + b > 0

However, this isn't true because:

For example:

a = 2 ; 2>0

b = -8 ; -8 < 0

2 + (-8) > 0

2 - 8 > 0

-6 > 0 ------> This is false, therefore the conjecture is false