Does $Q_i\rightarrow 0$ implies that $P\vee Q_i\rightarrow P$?

Question

Let $P$ be a projection on a Hilbert space $H$ and $\{Q_i\}_i$ is a decreasing net of projections on $H$. If $Q_i\rightarrow 0$, do we have $P\vee Q_i\rightarrow P$?

Whether $P\vee Q \perp P^\perp \wedge Q^\perp $?