Editing Deductive reasoning (section)

==== Modus tollens ====
{{Main|Modus tollens}}
Modus tollens (also known as "the law of contrapositive") is a deductive rule of inference. It validates an argument that has as premises a conditional statement (formula) and the negation of the consequent (<math>\lnot Q</math>) and as conclusion the negation of the antecedent (<math>\lnot P</math>). In contrast to [[modus ponens]], reasoning with modus tollens goes in the opposite direction to that of the conditional. The general expression for modus tollens is the following:

# <math>P \rightarrow Q</math>. (First premise is a conditional statement)
# <math>\lnot Q</math>. (Second premise is the negation of the consequent)
# <math>\lnot P</math>. (Conclusion deduced is the negation of the antecedent)

The following is an example of an argument using modus tollens:

# If it is raining, then there are clouds in the sky.
# There are no clouds in the sky.
# Thus, it is not raining.