Mind Your Ps and Qs

Here are 16 propositions involving a real number $x$:

1. $x\int^x_0 ydy < 0$
2. $x=0 $
3. $2\int^{x^2}_0ydy> x^2 $
4. $x^3> 1 $
5. $x> 1$
6. $0< x< 1 $
7. $x^2+4x+4 =0$
8. $x> 2$
9. $x< 0 $
10. $|x|> 1$
11. $x^2+x-2=0$
12. $\cos(x/2)> \sin(x/2)$
13. $x> 4$
14. $\int^x_0 \cos y dy =0$
15. $x=-2 $
16. $x=1$

[Note: the trig functions are measured in radians]


By choosing $p$ and $q$ from this list, how many correct mathematical statements of the form $p\Rightarrow q$ or $p\Leftrightarrow q$ can you make?


It is possible to rearrange the statements into four statements $p\Rightarrow q$ and four statements $p\Leftrightarrow q$. Can you work out how to do this?