"Missing $ Inserted" error in math environment

Question

I have the following .tex file:

\documentclass[convert={density=300,outext=.png}]{standalone}
\usepackage{standalone}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
$$\begin{array}{cc|c}
  A & B & A \land B\
  \hline
  F & F & F\
  F & T & F\
  T & F & F\
  T & T & T\
\end{array}$$ 
\end{document}

Previously, I had the {array} wrapped in a {displaymath} environment, but in both cases, attempting to compile this gives me the following errors:

! Missing $ inserted.
<inserted text> 
                $
l.8 $$\begin{array}{cc|c}

and

! Missing $ inserted.
<inserted text> 
                $
l.15 \end{array}
                $$

My understanding was that this arose from using math symbols outside of a math environment, but haven't I put the {array} in a math environment as is? It still generates the PDF as I expect, and outputs a .png thanks to the convert instructions defined in my {standalone}, but the compiler insists on showing me each of these error messages twice per compile.