1. Parse Trees

Hi, I've attached the question to this thread. For a) i've already done the tree but not sure how to find the truth value.
Here is a copy of the question if the attached question doesn't work. http://img837.imageshack.us/i/parsetrees.png/

2. Hello, brumby_3!

I'm not familiar with "Parse Trees",
. . but I can construct Truth Tables.

Construct the parse trees for the following
and use them to find the truth values when $\displaystyle p = T,\;q = T,\;r = F.$

$\displaystyle [1]\;\;p \tp \bigg[q \to (r \to p)\bigg]$

$\displaystyle \begin{array}{cccccccccccccc} p & | & q & | & r & || & p & \to & [q & \to & (r &\to & p)] \\ \hline T & | & T & | & F & || & T & \boxed{T} & T & T & F & T & T \\ \hline \\[-4mm] &&&&&& ^1 & ^4 & ^1 & ^3 & ^1 & ^2 & ^1 \end{array}$

$\displaystyle (2)\;\;(p \wedge q) \to (p \wedge r)$

$\displaystyle \begin{array}{cccccccccccccc} p & | & q & | & r & || & (p & \wedge & q) & \to & (p &\wedge & r) \\ \hline T & | & T & | & F & || & T & T & T & \boxed{F} & T & F & F \\ \hline \\[-4mm] &&&&&& ^1 & ^2 & ^1 & ^3 & ^1 & ^2 & ^1 \end{array}$

3. Hi Soroban,
For the first one, did you type the question out right by swapping some of the formulae around or is there a typo as it doesn't match my question. Also how do you know which is true and which is false? I mean the p q and r are obviously T, T and F as the question says but how do you know that the implies arrow is F? Also, what do the little numbers underneath each table represent? lol sorry for all the questions but this is my first time attempting these kind of questions.
Thanks kindly.

4. Hello, brumby_3!

I managed to misread/mistype the first one . . . *blush*

Construct the parse trees for the following
and use them to find the truth values when $\displaystyle p = T,\;q = T,\;r = F.$

$\displaystyle [1]\;\;p \to \bigg[q \vee (r \to p)\bigg]$

$\displaystyle \begin{array}{cccccccccccccc} p & | & q & | & r & || & p & \to & [q & \vee & (r &\to & p)] \\ \hline T & | & T & | & F & || & T & \boxed{T} & T & T & F & T & T \\ \hline \\[-4mm] &&&&&& ^1 & ^4 & ^1 & ^3 & ^1 & ^2 & ^1 \end{array}$

The small numbers indicate the order in which I filled in the table.