wanted to see if was right

[peicesr1]

(a) translate the argument into symbolic form and (b) determine if the argument is valid or invalid. You may compare to a standard form or use a truth table.

If the canteen is full, then wecan go for a walk.
We can go for a walk and will not get thirsty.
?If we go for a walk, then the canteen is not full.

P= if the canteen is full.
Q= we can go for a walk.

symbolic form is p->q [(p->q) conditional ~q]->
~q
?~p

valid

truth table

P l ql [(p->q) conditional ~q]->~p
t t t t t f f t f
t f t f f t t t f
f t f t t f f t t
f f f t f t t t t

 

[soroban]

Hello, peicesr1!

Your set-up is incomplete.

(a) Translate the argument into symbolic form.
(b) Determine if the argument is valid or invalid. You may compare to a standard form or use a truth table.

If the canteen is full, then we can go for a walk.
We can go for a walk and will not get thirsty.
If we can go for a walk, then the canteen is not full.

\(\displaystyle p\!:\;\text{the canteen is full}\)
\(\displaystyle q\!:\:\text{we can go for a walk}\)
\(\displaystyle r\!:\:\text{we get thirsty}\)

. . \(\displaystyle \begin{array}{cc}& p \,\to\,q \\ & q \:\wedge\,\sim\!r \\ \hline \therefore & q\,\to\,\sim\!p \end{array}\)


\(\displaystyle \begin{array}{c|c|c|| cccccccccccc} p & q & r & \big[(p & \to & q) & \wedge & (q & \wedge & \sim\!r)\big] & \to & (q & \to & \sim\!p) \\ \hline T&T&T \\ T&T&F \\ T&F&T \\ T&F&F \\ F&T&T \\ F&T&F \\ F&F&T \\ F&F&F \\ \hline \end{array}\)