Modus Ponens / Modus Tollens

Question 1

Modus Ponens

Answer 1

the principle that whenever a conditional statement and its antecedent are given to be true its consequent may be validly inferred

P.
Therefore, Q.

If P, then Q.

if it’s Tuesday this must be Belgium and it’s Tuesday so this must be Belgium

1.If today is Tuesday, then John will go to work.
2.Today is Tuesday.
3.Therefore, John will go to work.

If it is a car, then it has wheels. This is a car. Therefore it has wheels.

Question 2

Modus Tollens

Answer 2

Modus tollens is a mixed hypothetical syllogism that takes the form of “If P, then Q. Not Q. Therefore, not P.” It is an application of the general truth that if a statement is true, then so is its contrapositive.

If P, then Q
Not Q,
Therefore, not P

If there is smoke, there is fire. There is not fire, so there is no smoke.

If I am happy, then I smile. I am not smiling, therefore I am not happy.