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I got my midterm back today and I got 0 on the following question. There was no comments on this question at all from the marker.

For propositional formulas A and B, prove (or disprove) that if $A\models \lnot B $ is true then $\vdash_H \lnot(A\rightarrow\lnot B)$

Can someone tell me if the answer is true or not?

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    I suspect that the point of it being true or not matters less to your instructor than does *HOW* you arrived at your answer. Why don't you post your work, and ask whether your proof is sound?2012-11-27
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    I'm sure 1 mark is given for saying it's true or not and my proof was quite long.2012-11-27

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Hint: Put $p$ for $A$ and $\neg p$ for $B$. Now ask: is $A\models \lnot B$ true? Is $\vdash_H \lnot(A\rightarrow\lnot B)$ true?

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    That depends on whether $H$ is consistent, it seems.2012-11-27
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    Indeed it certainly will! But I thought this would be a good simple question with which to probe $H$ (revealing something significant, whichever answer we get).2012-11-27
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    @user44322 What more did you write?2012-11-27