This is formula which I must write as CNF, DNF and Negation of formula as CNF and DNF: $$(p \rightarrow (q \rightarrow r)) \rightarrow ((p \rightarrow \neg r) \rightarrow (p \rightarrow \neg q))$$

After I get rid of the implications I got something like this (DNF FORM): $$(p \wedge q \wedge r) \vee (p \wedge \neg r) \vee \neg p \vee \neg q$$

And this is the answer in my book, but what's the difference between a good answer and Wolfram's?

One more question. How can i turn it to CNF ?

  • $\begingroup$ The difference is that your answer, if correct, isn't fully simplified which isn't to say it is wrong. $\endgroup$ – Git Gud Jun 17 '15 at 12:54
  • $\begingroup$ Could some help me how can i create from this CNF form? $\endgroup$ – hadson172 Jun 17 '15 at 13:02

Note that $(p→(q→r))→((p→¬r)→(p→¬q))$ is a tautology.

There's a typo in your wolfram input. It should look like this, with the $r$ in $(p \rightarrow \neg r)$ negated.

But your simplification is correct. It can be further simplified though.


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