Let Q be the linearly ordered set of rational numbers considered as a category while $R^{+}$ is the set of reals with $\infty$. In $Sets^{Q}$,prove that the subobject classifier $\Omega$ has $\Omega(q)=\{$$r| r\in$ $R^{+}$ , $r\geq q$ $\}$
I'm not sure how to start. Should I find the natural transformations needed in the pullback and then prove uniqueness of $\phi$: P $\implies$ $\Omega$?
I've been trying to find an analogy with the S.C in $Sets^{C^{op}}$ but without good results.
I'd appreciate hints rather than complete solutions.