How to typeset contradiction symbol?

You might add a negativ space \! which results in no space between the two symbols:

\documentclass{article}
\begin{document}
\[
\Rightarrow\!\Leftarrow
\]
\end{document}

As @Rethliopuks noted in the comments, the package tipa disables the usage of \! in mathmode as negative space. If you use this package (or any other package which disables \!) you might use

\Rightarrow\mskip-\thinmuskip\Leftarrow

instead for the same results (\mskip-\thinmuskip is the default definition of \!).

That gives what you want (added \!):

\documentclass{article}
\begin{document}
\[
\Rightarrow\!\Leftarrow
\]
\end{document}