The discussion clarifies that providing a single example, such as m=1 and n=2, is insufficient to prove the statement that for all integers m and n, m+n≠10. This is because a single counterexample does not negate the existence of other integers that could satisfy the equation m+n=10, such as m=4 and n=6. The conclusion emphasizes that to disprove a universal quantifier, one must demonstrate the existence of at least one counterexample, while proving it requires showing that no such integers exist.
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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.ver_mathstats said: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?
Homework Equations
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?