In logic, modus ponens (Latin: mode that affirms; often abbreviated MP) is a valid, simple argument form. It is a very common form of reasoning, and takes the following form:

If P, then Q.

P.

Therefore, Q.

In logical operator notation:
P → Q
P
⊢ Q

where ⊢ represents the logical assertion ("Therefore Q is true").
The modus ponens rule may also be written:


In logic, Modus tollens (Latin for "mode that denies") is the formal name for indirect proof or proof by contrapositive (contrapositive inference), often abbreviated to MT.

If P, then Q.

Q is false.

Therefore, P is false.

Or in set-theoretic form:
P ⊆ Q
x ∉ Q
∴ x ∉ P
("P is a subset of Q. x is not in Q. Therefore, x is not in P.")