Modus Tollens (Rain Example)
P → Q, ¬Q ⊢ ¬P | "If it's raining, then the ground is wet. The ground is not wet. Therefore, it's not raining."
Modus Ponens (Study Example)
P → Q, P ⊢ Q | "If you study hard, then you pass the exam. You study hard. Therefore, you pass the exam."
Disjunctive Syllogism (Transport Example)
P ∨ Q, ¬P ⊢ Q | "I go by car or by bus. I don't go by car. Therefore, I go by bus."