For proposition A "I work" , B "I study " C "I passed math exam"
State the validity of the reasoning
1.I'm not studying if I work
２.I work or pass the math exam
３.I I passed the math exam. So I studied
1.$A \implies \sim B$
2.$A \lor C$
3.$C \implies B$
$C \implies B$ also means $\sim B \implies \sim C$ ,
$A \implies \sim B \implies \sim C$
$A \implies\sim C$= $\sim A \lor \sim C$
is this enough to proof?