'\\' and '\newline' not working

Question

Those two symbols in the tite aren't working and I have no idea what's going on. This is my first time using latex so I'm lost. Also, can someone teach me how to make a bullet like the one in Microsoft Word? Here's my text:

%% logical symbols
% \land     /\
% \lor      \/
% \lnor     (negation)
% \to       ->
% \lequiv   <->
% \models   |=

...

\begin{solution}
$$(P \to (\lnot Q \land R)) \land (P \to \lnot Q)$$
$${With: \hspace{1cm} (\lnot P \lor \lnot Q) \land (\lnot P \lor R) \land (\lnot P \lor \lnot Q)}$$
$${ 
Without : T1 \lequiv T2 \land T4 \\
– T2 \lequiv P \to T3 \\
– T3 \lequiv \lnot Q \land R \\
– T4 \lequiv P \to \lnot Q \\
– F1 : (T1 \land T2 \land T4) \lor (\lnot T1 \land :T2) \lor (\lnot T1 \land \lnot T4) \\
– F2 : (T2 \land \lnot P) \lor (T2 \land T3) \lor (\lnot T2 \land P \land \lnot T3) \\
– F3 : (T3 \land \lnot Q \land R) \lor (\lnot T3 \land Q) \lor (\lnot T3 \land \lnot R) \\
– F4 : (T4 \land \lnot P) \lor (T4 \land \lnot Q) \lor (\lnot T4 \land P \land Q) \\
Final result: T1 \land F1 \land F2 \land F3 \land F4 }$$
\end{solution}

Answer 1

$$ is not latex syntax, but if you do use it it is essentially the same as \[...\] and that is a single line display, you can not use \\ to get multiple lines.

Use the amsmath package and an align or similar enviornment for multi-line displays.

It was rather hard to guess the intended layout but something like

\documentclass{article}

\usepackage{amsmath,amssymb}
\newcommand\lequiv{\iff}

\begin{document}

\begin{align*}
&(P \to (\lnot Q \land R)) \land (P \to \lnot Q)\\
\text{With}:&\, (\lnot P \lor \lnot Q) \land (\lnot P \lor R) \land (\lnot P \lor \lnot Q)\\
\text{Without}:&\, T1 \lequiv T2 \land T4 \\
&\,T2 \lequiv P \to T3 \\
&\,T3 \lequiv \lnot Q \land R \\
&\,T4 \lequiv P \to \lnot Q \\
F1 :&\, (T1 \land T2 \land T4) \lor (\lnot T1 \land :T2) \lor (\lnot T1 \land \lnot T4) \\
F2 :&\, (T2 \land \lnot P) \lor (T2 \land T3) \lor (\lnot T2 \land P \land \lnot T3) \\
 F3 :&\, (T3 \land \lnot Q \land R) \lor (\lnot T3 \land Q) \lor (\lnot T3 \land \lnot R) \\
F4 :&\,(T4 \land \lnot P) \lor (T4 \land \lnot Q) \lor (\lnot T4 \land P \land Q) \\
\text{Final result}:&\, T1 \land F1 \land F2 \land F3 \land F4 
\end{align*}
\end{document}