I have this question

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As per http://web.stanford.edu/class/cs103/tools/truth-table-tool/

This statment is not a tautuology.So is the question wrong?

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  • $\begingroup$ It looks like you're using tool you don't understand how to use. RTFM and write "(P->Q)->(Q->R)->(P or Q->R)" instead into your tool. The expression you entered have four independent atoms P, PvQ, Q and R. $\endgroup$ – skyking Sep 16 '15 at 9:37

Row $5$ has $P$ and $Q$ set to false, and $P\lor Q$ set to true. That's not possible.

Also, clarify whether $a\implies b\implies c$ mean $$(a\implies b)\implies c$$ or $$a\implies (b\implies c)$$ because they are not the same.

To get proof that you have a tautology, insert

(P->R) -> (Q->R) -> ((P\/Q) -> R)

into the webpage you listed.

  • $\begingroup$ You were faster than I was! haha +1 $\endgroup$ – Patrick Da Silva Sep 16 '15 at 9:25
  • $\begingroup$ @5xum On trying to solve manually first i need to write the truth values for the triple.By using 2^3 i understand that there a 8 possible values.But how can i write these values easily.is there an easy way? $\endgroup$ – techno Sep 16 '15 at 9:46
  • $\begingroup$ @techno Is writing $8$ possible values not an easy way? $\endgroup$ – 5xum Sep 16 '15 at 10:53
  • $\begingroup$ @5xum Yeah.But how can i easy write the triplet pattern?Is there an easy way to follow? $\endgroup$ – techno Sep 17 '15 at 5:44
  • $\begingroup$ @techno Yes. The last column goes $TFTFTFTF\dots$. The column before that goes $TTFFTTFFTTFF\dots$. The one before that goes $TTTTFFFFTTTTFFFF\dots$. If you continue with more variables, the next one has $8$ repetitions of $T$ and $8$ of $F$, then $16$, then $32$,\dots $\endgroup$ – 5xum Sep 17 '15 at 5:49

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