Truth table logic Can someone please show me how this works, i'm going out of my mind
I know the truth tables for the individual AND, OR AND NOT but when it comes to them being combined my understanding is shattered into pieces =/ 

 A: Take it one step at a time, creating extra columns if needed.
For example, for $p \lor (q \land \lnot p)$: 


*

*Make your $p, q$ columns as you did. 

*Then create a column for $\color{blue}{\lnot p}$, and fill in the truth values (reversing the truth values that are listed in the "p-column"

*Then create a column headed by $q \land \color{blue}{\lnot p}$, "and-ing" the $q$-column and the $\lnot p$-column. 

*Finally, create a column headed with $p \lor (q\land \lnot p),$"or-ing" the $p$-column and the $(q \land \lnot p) column.
That way you're just needing to focus on one connective at a time.
A: Before getting into the truth table let's clarify the following statements:
$P \wedge Q$ is true when $P$ and $Q$ are the same , for instance: 
if $P$ is TRUE and $Q$ is FALSE $P \wedge Q$ returns FALSE.
Moreover: if $P$ is FALSE and $Q$ is FALSE $P \wedge Q$ returns TRUE.
Negation $\neg$ will set the opposite value to the variable.
For instance, if $P$ is FALSE $\neg P$ (Not P) will return TRUE.
From this, we can conclude that if $P \neq Q$ then $P = \neg Q$.
Disquction (or) will return TRUE if any of the variables are TRUE.
if $P$ is FALSE and $Q$ is TRUE then $P \vee Q$ will return TRUE.
if $P$ is FALSE, $Q$ is FALSE and $S$ is TRUE then again $P \vee Q \vee S$ will return TRUE.
Now, regarding your question, you can try to make your life a little easier by setting the inner parenthesis as another boolean variable.
Example:
If $P$ is TRUE and $Q$ is FALSE:
In the logic statement $P \vee (Q \wedge \neg P)$ :
Let $A$ be  $\neg P$ .
Since $P$ is TRUE , $\neg P$ returns FALSE.
let $B$ be $Q \wedge A$.
Since $Q$ is FALSE and A is FALSE, $Q \wedge A$ returns FALSE.
So, $P \vee (Q \wedge \neg P)$ 
will return TRUE, since $P$ is TRUE and the whole parenthesis is FALSE. 
This example is the result of your 3rd line, if I'm correct.
A: First since you have 2 variables the table will have 4 rows. First you complete the column under p,q such that all 4 cases appear. Then you complete the column for $r=\lnot{p}$. Then using the column for q and the column for r you complete the column for $s=(q\land r)$.
Finally using the column for p and the column for s you complete the column for $(p \lor s)$.
In each step you use the truth tables for AND, OR, NOT you already know.
Does this help?
