A scheme in LaTeX

Question

I have 5 statements and some of them are equivalent, for some of them implications hold only in one direction. I would like to draw the scheme of these relations in LaTeX. Fortunately, two pairs of these statements are equivalent, so the scheme will not be overloaded with arrows.

In fact, there will be a triangle with 3 nodes (1),(2),(3) with some arrows between them, and (4) will have just a connection with (2), (5) will have the only connection with (3).

How to draw it in LaTeX? Here is an example from Visio: however I need arrows to be without corners and like $\Rightarrow$ or $\Leftrightarrow$.

Answer 1

This is the closest to $\Rightarrow$ I found. I was too lazy, so it's with absolute positioning ;)

EDIT: Should have read the question. Now with only one connection between 2/4 and 3/5

\documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{figure}
\begin{center}
\begin{tikzpicture}
\node[draw,circle] (s1) at (0,0) {1};
\node[draw,circle] (s2) at (-1.6,-2) {2};
\node[draw,circle] (s3) at (1.6,-2) {3};
\node[draw,circle] (s4) at (-4,-3) {4};
\node[draw,circle] (s5) at (4,-3) {5};
\path
    (s2) edge[->, double distance=1pt, >=latex', bend left=40] (s1)
    (s3) edge[->, double distance=1pt, >=latex', bend right=40] (s1)
    (s3) edge[->, double distance=1pt, >=latex', bend left=60] (s2)
    (s2) edge[<->, double distance=1pt, >=latex'] (s4)
    (s3) edge[<->, double distance=1pt, >=latex'] (s5);
\end{tikzpicture}
\end{center}
\caption{Five strange statements.}
\label{fig1}
\end{figure}
\end{document}

Answer 2

OK, I'm not sure I fully understand the question, but here's a possible answer using TikZ...

Edited: I'm not very experienced with figures; here's something "that appears to work", and incorporates @Nikolaus Mayer's (+1) arrows. Note that figures are floats, so your figure, rather than disappearing, may have just moved to a less convenient point in your document...

\documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{figure}
\begin{center}
\begin{tikzpicture}[>=latex,every node/.style={draw,circle,minimum width={3em},node distance=6em}]
\node (a) {1};
\node [below left of=a] (b) {2}; 
\node [below left of=b] (d) {4}; 
\node [below right of=a] (c) {3}; 
\node [below right of=c] (e) {5}; 
\draw [->] (b) -- (a);
\draw [->] (c) -- (a);
\draw [->] (c) -- (b);
\draw [<->] (b) -- (d);
\draw [<->] (c) -- (e);
\end{tikzpicture}
\caption{This is a figure}
\end{center}
\end{figure}
\end{document}