Question about logical form of a statement Consider the following statement:

Jane saw a police officer, and Roger saw one too.

Logical form of the statement above (provided by the book):
$$\exists x\big(P(x) \land S( j, x)\big) \land \exists y\big(P(y) \land S(r, y)\big)$$
Where $P(x)$ stands for “$x$ is a police officer”, $S(x, y)$ stands for “$x$ saw $y$”, $j$ stands for Jane, and $r$ stands for Roger.
Question is, assume I want to clearly show that the police officer that Roger saw was not the one that Jane saw, how do I do it?

You can write
$$\exists x\big(P(x) \land S( j, x) \big) \land \exists y\big(P(y) \land S(r, y) \land \lnot S(j,y)\big)$$
So, Jane didn't see $y$ but Roger did. So if we take both $x$ and $y$ to be the same, we have 
$$P(a) \land S(j,a) \land P(a) \land S(r,a) \land \lnot S(j,a)$$
which is a contradiction ($S(j,a) \land \lnot S(j,a)$).
