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Evidence are simply facts to support a claim, while counterexamples are instances to show the contradictions in a claim
<em>The question is incomplete, as the required drop-down menus are missing. So, I will give a general explanation</em>
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To show that a statement is true, you need evidence.
Take for instance:
The evidence that the above proof is true is by taking the <em>squares of both sides of </em>
However, a counterexample does not need a proof per se.
What a counterexample needs is just an instance or example, to show that:
An instance to prove that: is false is:
Hence, the complete statement could be:
<em>In a direct proof, evidence is used to support a proof . On the other hand, a counterexample is a single example that shows that a proof is false.</em>
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Read more about evidence and counterexample at: