Modus Ponens: (Latin for: mood that affirms.) In its basic form, an argument that runs ‘If p, then q. p. Therefore q.’
If today is Tuesday, then I will go to work.
Today is Tuesday.
Therefore, I will go to work.
Modus Tollens: (Latin for: mood that denies.) In its basic form, an argument that runs ‘If p, then q. But not-q. Therefore not-p.’
If I miss the train, I take a taxi.
I didn’t take a taxi.
Therefore, I didn’t miss the train.
Definitions, but not examples, taken from Antony Flew, ed., A Dictionary of Philosophy, rev. 2nd ed., 236.