Propositional Logic (converting sentence to formula)

Question

How do I put this into a formula? If Jones drove the car, Smith is innocent. If Brown fired the gun, then Smith is not innocent. Jones did not drive the car. I put $(J\Rightarrow S)\vee (B\Rightarrow \neg S)$ Can anyone let me know if this is right or wrong? And if wrong, what the right one would be?

Answer 1

Let's name some statements.

$ \mathcal{J}$ : Jones drove the car.

$ \mathcal{S}$ : Smith is innocent.

$ \mathcal{B}$ : Brown fired the gun.

Then, if you convert those sentences, you would get

$$(\mathcal{J}\Rightarrow \mathcal{S}) \wedge (\mathcal{B}\Rightarrow \neg \mathcal{S}) \wedge (\neg \mathcal{J})$$