Show that $((pLeftrightarrow q)Leftrightarrow T)$ and $(pLeftrightarrow (qLeftrightarrow T))$ are logically...












0












$begingroup$


I tried this but I'm not sure what to do about the T value:



$$((pLeftrightarrow q ) Leftrightarrow T ) equiv neg p Leftrightarrow neg q Leftrightarrow T equiv neg p Leftrightarrow neg (neg q Leftrightarrow neg T) equiv neg p Leftrightarrow (q Leftrightarrow T)$$



Am I using the rules correctly?






logic propositional-calculus







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  • 1




    $begingroup$
    How about a truth table?
    $endgroup$
    – Umberto P.
    Jan 29 at 19:03










  • $begingroup$
    I already did the truth table for question A but B asks to do it with transformations
    $endgroup$
    – memelord420xd
    Jan 29 at 21:11










  • $begingroup$
    @memelord420xd what transformation rules do you have available?
    $endgroup$
    – Bram28
    Feb 1 at 1:48
















0












$begingroup$


I tried this but I'm not sure what to do about the T value:



$$((pLeftrightarrow q ) Leftrightarrow T ) equiv neg p Leftrightarrow neg q Leftrightarrow T equiv neg p Leftrightarrow neg (neg q Leftrightarrow neg T) equiv neg p Leftrightarrow (q Leftrightarrow T)$$



Am I using the rules correctly?






logic propositional-calculus







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    How about a truth table?
    $endgroup$
    – Umberto P.
    Jan 29 at 19:03










  • $begingroup$
    I already did the truth table for question A but B asks to do it with transformations
    $endgroup$
    – memelord420xd
    Jan 29 at 21:11










  • $begingroup$
    @memelord420xd what transformation rules do you have available?
    $endgroup$
    – Bram28
    Feb 1 at 1:48














0












0








0





$begingroup$


I tried this but I'm not sure what to do about the T value:



$$((pLeftrightarrow q ) Leftrightarrow T ) equiv neg p Leftrightarrow neg q Leftrightarrow T equiv neg p Leftrightarrow neg (neg q Leftrightarrow neg T) equiv neg p Leftrightarrow (q Leftrightarrow T)$$



Am I using the rules correctly?






logic propositional-calculus







share|cite|improve this question











$endgroup$




I tried this but I'm not sure what to do about the T value:



$$((pLeftrightarrow q ) Leftrightarrow T ) equiv neg p Leftrightarrow neg q Leftrightarrow T equiv neg p Leftrightarrow neg (neg q Leftrightarrow neg T) equiv neg p Leftrightarrow (q Leftrightarrow T)$$



Am I using the rules correctly?






logic propositional-calculus




logic propositional-calculus






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 29 at 21:13







memelord420xd

















asked Jan 29 at 18:58









memelord420xdmemelord420xd

61




61








  • 1




    $begingroup$
    How about a truth table?
    $endgroup$
    – Umberto P.
    Jan 29 at 19:03










  • $begingroup$
    I already did the truth table for question A but B asks to do it with transformations
    $endgroup$
    – memelord420xd
    Jan 29 at 21:11










  • $begingroup$
    @memelord420xd what transformation rules do you have available?
    $endgroup$
    – Bram28
    Feb 1 at 1:48














  • 1




    $begingroup$
    How about a truth table?
    $endgroup$
    – Umberto P.
    Jan 29 at 19:03










  • $begingroup$
    I already did the truth table for question A but B asks to do it with transformations
    $endgroup$
    – memelord420xd
    Jan 29 at 21:11










  • $begingroup$
    @memelord420xd what transformation rules do you have available?
    $endgroup$
    – Bram28
    Feb 1 at 1:48








1




1




$begingroup$
How about a truth table?
$endgroup$
– Umberto P.
Jan 29 at 19:03




$begingroup$
How about a truth table?
$endgroup$
– Umberto P.
Jan 29 at 19:03












$begingroup$
I already did the truth table for question A but B asks to do it with transformations
$endgroup$
– memelord420xd
Jan 29 at 21:11




$begingroup$
I already did the truth table for question A but B asks to do it with transformations
$endgroup$
– memelord420xd
Jan 29 at 21:11












$begingroup$
@memelord420xd what transformation rules do you have available?
$endgroup$
– Bram28
Feb 1 at 1:48




$begingroup$
@memelord420xd what transformation rules do you have available?
$endgroup$
– Bram28
Feb 1 at 1:48










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    $begingroup$

    Hint: $quad r equiv (rleftrightarrow top)$






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      Hint: $quad r equiv (rleftrightarrow top)$






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        Hint: $quad r equiv (rleftrightarrow top)$






        share|cite|improve this answer









        $endgroup$



        Hint: $quad r equiv (rleftrightarrow top)$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Jan 29 at 23:06









        Graham KempGraham Kemp

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