# Thread: laws of logic question

1. ## laws of logic question

hey guys, i have this question.

$(((p \rightarrow r ) \rightarrow p ) \wedge q ) \wedge (-((p \rightarrow r ) \rightarrow p ))$

my answer after simplifing boths sides i got

$(p \wedge q ) \wedge (-p)$

which then using associative law gives

$q \wedge ( p \wedge -p )$

then inverse law

$q \wedge T$

then Annihilation law

$T$

so this is a tautology. Can anyone confirm this is correct? thanks!

2. You lost me at your "inverse law" step. Does that big "T" mean p and not p is true for all values of p?

3. Originally Posted by ANDS!
You lost me at your "inverse law" step. Does that big "T" mean p and not p is true for all values of p?
I think i just made a mistake. Its ment to be $F$ not $T$

so that would make the final answer $F$, so its a contradiction.. ?

4. It would be a contradiction if this were an actual proof and you implied something (namely that it is not the case that if p then r implies p). All I see is that this is false for all values of p, q, and r, since p and not p can never be true.

At least you recognize contradiction here, and you deduced (or I assume you did) that if p then r implies p.