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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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  • $\begingroup$ 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? $\endgroup$
    – amWhy
    Nov 27, 2012 at 3:16
  • $\begingroup$ I'm sure 1 mark is given for saying it's true or not and my proof was quite long. $\endgroup$
    – user44322
    Nov 27, 2012 at 3:25

1 Answer 1

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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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  • $\begingroup$ That depends on whether $H$ is consistent, it seems. $\endgroup$
    – hmakholm left over Monica
    Nov 27, 2012 at 13:56
  • $\begingroup$ 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). $\endgroup$
    – Peter Smith
    Nov 27, 2012 at 15:08
  • $\begingroup$ @user44322 What more did you write? $\endgroup$
    – Peter Smith
    Nov 27, 2012 at 21:31

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