Contraposition

In logic, contraposition is an inference that 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 P → Q {displaystyle P ightarrow Q} is thus ¬ Q → ¬ P {displaystyle eg Q ightarrow eg P} . For instance, the proposition 'All cats are mammals' can be restated as the conditional 'If something is a cat, then it is a mammal'. The law of contraposition says that statement is true if, and only if, its contrapositive 'If something is not a mammal, then it is not a cat' is true. In logic, contraposition is an inference that 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 P → Q {displaystyle P ightarrow Q} is thus ¬ Q → ¬ P {displaystyle eg Q ightarrow eg P} . For instance, the proposition 'All cats are mammals' can be restated as the conditional 'If something is a cat, then it is a mammal'. The law of contraposition says that statement is true if, and only if, its contrapositive 'If something is not a mammal, then it is not a cat' is true.