Propositional Logic Homework Check: Proving B's Guilt

[TheFurryGoat]

Homework Statement

Either A or B (names changed) stole the exam answers. Formalize these and check if this is a correct deduction:
1) If A didn't meet B for lunch, then B is guilty or A lives in the countryside
2) If B isn't guilty, then A didn't meet B for lunch and the incident happened after dinner
3) If it happened after dinner, then B is guilty, or A lives in the countryside
4) It rained in the evening, and the teacher slept sound asleep
5) And so, B is guilty

The Attempt at a Solution

"A met B for lunch" = P
"B is guilty" = Q
"A lives in the countryside" = R
"it happened after dinner" = S
"It rained in the evening" = T
"the teacher slept sound asleep" = U

Not actually sure but am I supposed to prove or disprove this? :

$$P \rightarrow Q \vee R, \neg Q \rightarrow \neg P \wedge S, S \rightarrow Q \vee R, T \wedge U \models Q$$

 

[CompuChip]

Yep, that looks about right.

Actually, T and U sound completely irrelevant, and you can probably reduce it to
$$\{ P \rightarrow Q \vee R, \neg Q \rightarrow \neg P \wedge S, S \rightarrow Q \vee R \} \models Q$$