The counterexample can be written algebraically as x+y ≤ x-y.
Counterexample: 5 and - 2
Practice makes perfect
Let's call the two numbers x and y. We can write the sum and difference of these numbers as follows.
x+y and x-y
Let's write the conjecture first.
The sum of two numbers
is always greater than their difference
⇓
x+y > x-y
The counterexample to this is if the sum of x and y is less than or equal to the difference of x and y.
Counterexample:& x+y≤ x-y
By solving the inequality of the counterexample, we can determine under what conditions the counterexample applies.
Whenever the number you are adding and subtracting is less than or equal to 0, the conjecture is false. Let's use an example where x=5 and y=- 2.
Sum of Numbers:& 5+(- 2)= 3
Difference of Numbers:& 5-(- 2)= 7
Counterexample:& 3 < 7
