LaTeX table - extra alignment tab?

Question

I'm new to LaTeX and trying to make a truth table, but it won't compile. When I try to run the code, it says "Extra alignment tab has been changed to \cr." Here is my code:

\item (Textbook 1.1/38, 4 points) $((p\rightarrow q)\rightarrow r)\rightarrow s$
\begin{center}
\begin{tabular}{c|c|c|c|c|c}
\hline
$p$ & $q$ & $r$ & $s$ & $p\rightarrow q$ & $(p\rightarrow q)\rightarrow$ r & $((p\rightarrow q)\rightarrow r)\rightarrow s$ \\ 
\hline
T & T & T & T & T & T & T \\
T & T & T & F & T & T & F \\
T & T & F & T & T & F & T \\
T & F & T & T & F & T & T \\
T & F & T & F & F & T & F \\
T & F & F & T & F & T & T \\
T & F & F & F & F & T & F \\
F & T & T & T & T & T & T \\
F & T & T & F & T & T & F \\
F & T & F & T & T & F & T \\
F & T & F & F & T & F & T \\
F & F & T & T & T & T & T \\
F & F & T & F & T & T & F \\
F & F & F & T & T & F & T \\
F & F & F & F & T & F & T \\
\hline
\end{tabular}
\end{center}

Answer 1

Very easily, you declared six columns: there are six c in the line

\begin{tabular}{c|c|c|c|c|c}

Then, every line of your table has seven cells instead:

...
T & T & T & T & T & T & T \\
...

So, you should solve by changing

\begin{tabular}{c|c|c|c|c|c}

to

\begin{tabular}{c|c|c|c|c|c|c}

or

\begin{tabular}{c*{6}{|c}}