Contraposition
In logic,
contraposition is a law, which says that a conditional statement is logically equivalent to its
contrapositive. The contrapositive of the statement has its antecedent and consequent inverted and flipped: the contrapositive of is thus. For instance, the proposition "
All bats are mammals" can be restated as the conditional "
If something is a bat, then it is a mammal". Now, the law says that statement is identical to the contrapositive "
If something is not a mammal, then it is not a bat." The contrapositive can be compared with three other relationships between conditional statements: ▪
Inversion: . "
If something is not a bat, then it is not a mammal." Unlike the contrapositive, the inverse's truth value is not at all dependent on whether or not the original proposition was true, as evidenced here. The inverse here is clearly not true. ▪
Conversion: . "
If something is a mammal, then it is a bat." The converse is actually the contrapositive of the inverse and so always has the same truth value as the inverse, which is not necessarily the same as that of the original proposition. ▪
Negation:.