# Example for Proofs

## Homework Statement

Suppose you are asked to prove that for all integers m and n, m+n≠10. You give the example m=1 and n=2. Why is this not sufficient?

## The Attempt at a Solution

I can't quite understand why it is not sufficient? Could someone please explain to me why is it insufficient?

fresh_42
Mentor

## Homework Statement

Suppose you are asked to prove that for all integers m and n, m+n≠10. You give the example m=1 and n=2. Why is this not sufficient?

## The Attempt at a Solution

I can't quite understand why it is not sufficient? Could someone please explain to me why is it insufficient?
What do you mean? ##m+n\neq 10## isn't true for some integers. It is sufficient to say ##4+6=10## in order to disprove it. As it cannot be proven, there cannot be a sufficient condition for a proof either.

An example is never sufficient to prove an all quantifier, only to disprove one.

Orodruin
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
Put slightly differently, you are asked to show that no integers n and m exist that satisfy n+m = 10. Then it is not enough to give a single example of integers that do not sum to 10 as another pair of integers could do that (and does).