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I think I saw a strategy to prove this statement is to suppose $a$ and $b$ are true then to prove that $c$ is false. Is it correct?

user546106
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  • No, that won’t work. The techniques I have seen are along the lines of “Let $a$ be true and assume $b$ is false.” Now prove $c$ must be true. – Clayton Apr 08 '18 at 16:08
  • @Clayton Thank you. I remember it now. That's what I read. – user546106 Apr 08 '18 at 16:15

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No. If you suppose $a$ and $b$ are both true, then you've already assumed what you need to prove, since under those circumstances we have $b$ or $c$ being true anyway.

You must assume $a$ and then show that either one of $b$ or $c$ is true; or you must assume $b$ and $c$ are both false, and show that $a$ is false. One strategy for the former, as pointed out by @Clayton in the comments: show that if $a$ is true and $b$ is false, then $c$ is true. One strategy for the latter: assume that $a$ is true but $b$ and $c$ are both false, and then derive a contradiction.

Patrick Stevens
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