\documentclass[12pt]{article}
\usepackage{fullpage}
\usepackage{amsmath,amssymb,amsfonts}

\parindent 0in

\newcommand{\NN}{\mathbb{N}}              % Natural numbers
\newcommand{\QQ}{\mathbb{Q}}              % Rationals
\newcommand{\RR}{\mathbb{R}}              % Reals
\newcommand{\ZZ}{\mathbb{Z}}              % Integers
\newcommand{\powerset}{\mathcal{P}}       % power set
\newcommand{\setcomp}[1]{\overline{#1}}   % set complement
\newcommand{\negate}{{\sim}}              % negation (logic)
\newcommand{\xor}{\oplus}                 % xor

\renewcommand{\implies}{\Rightarrow}      % shorter version of =>
\renewcommand{\iff}{\Leftrightarrow}      % shorter <=>

\begin{document}

Use a truth table to prove the following logical equivalence.
\begin{displaymath}
  P \wedge (Q \vee R) \equiv (P \wedge Q) \vee (P \wedge R)
\end{displaymath}
Solution:

\begin{displaymath}  % start unumbered math environment
  %
  % Start a table in math mode.  The |c|c|c|c|c|c|c|c| string is a
  % format string that says there will be 8 colunms in the table.  The
  % c's indicate that the data in each column will be centered (use l
  % for left justified and r for right justified).  The vertical bar
  % means that lines will be drawn between columns.  The trailing
  % \hline causes a horizontal line to be drawn across the top of the
  % table.
  %
  \begin{array}{|c|c|c|c|c|c|c|c|}\hline
    %
    % Each row of the table consists of data separated by "&" symbols.
    % Each row must end with "\\" to cause a newline.  A trailing
    % \hline will cause a line to be drawn under the row.  A double
    % \hline is often used to separate the table header from the rest
    % of the table. 
    %
    P & Q & R & Q \vee R & P \wedge (Q \vee R) & P \wedge Q & P \wedge
    R & (P \wedge Q) \vee (P \wedge R)\\\hline\hline
    T & T & T & T & \mathbf{T} & T & T & \mathbf{T}\\\hline
    T & T & F & T & \mathbf{T} & T & F & \mathbf{T}\\\hline
    T & F & T & T & \mathbf{T} & F & T & \mathbf{T}\\\hline
    T & F & F & F & \mathbf{F} & F & F & \mathbf{F}\\\hline
    F & T & T & T & \mathbf{F} & F & F & \mathbf{F}\\\hline
    F & T & F & T & \mathbf{F} & F & F & \mathbf{F}\\\hline
    F & F & T & T & \mathbf{F} & F & F & \mathbf{F}\\\hline
    F & F & F & F & \mathbf{F} & F & F & \mathbf{F}\\\hline
  \end{array}
\end{displaymath}

\end{document}
