# Hamilton equations-Symplectic scheme

We know that $$dot{q} = frac{partial H}{partial p}$$ and $$dot{p} = -frac{partial H}{partial q}$$, and we also know the values $$Q$$ and $$P$$ respectively of $$q$$ and $$p$$ at a later time step $$Delta t$$. How could we prove that the quantities
begin{align} Q &= q + {Delta}tfrac{partial H}{partial p}(q,p),\ P &= p – {Delta}tfrac{partial H}{partial q}(q,p) end{align}
are not symplectic, while
begin{align} Q &= q – {Delta}tfrac{partial H}{partial p}(q,p),\ P &= p + {Delta}tfrac{partial H}{partial Q}(Q,p) end{align}
are symplectic?

Clarification:
The sets of equations define different numerical integrators: in the first case (qi+1,pi+1) directly in terms of (qi,pi), and in the second case qi+1 in terms of (qi,pi), and pi+1 in terms of (qi+1,pi).