If A @ B means A is the son of B, A # B means A is the brother of B and A B means A is the mother of B, then what does P @ Q R # S mean?

Let's decode the expression $P\text{@}Q\ast R\#S$ step-by-step from left to right:
1. $P\text{@}Q⟹P$ is the son of $Q$ ($\text{Male}$).
2. $Q\ast R⟹Q$ is the mother of $R$ ($\text{Female}$).
3. $R\#S⟹R$ is the brother of $S$ ($\text{Male}$).

From components (2) and (3), $Q$ is the mother of both $R$ and $S$, so $R$ and $S$ are siblings.
From component (1), $P$ is the son of $Q$. Since $Q$ is the mother of $S$, $P$ must be the brother of $S$.

Therefore, $P$ is the brother of $S$.