kontrapositivitet

Kontrapositivitet refers to a logical equivalence in propositional logic. A conditional statement of the form "If P, then Q" (symbolized as P → Q) is logically equivalent to its contrapositive, which is "If not Q, then not P" (symbolized as ¬Q → ¬P). This means that the truth value of the original statement is always the same as the truth value of its contrapositive. If one is true, the other is true, and if one is false, the other is false.

The contrapositive is derived by negating both the antecedent (P) and the consequent (Q) of the original conditional statement and then reversing their order. For example, if the statement is "If it is raining, then the ground is wet," its contrapositive is "If the ground is not wet, then it is not raining." Both statements convey the same logical relationship.

Understanding contrapositivitet is important in logic and mathematics for proving theorems. Sometimes it is easier to prove the contrapositive of a statement than the original statement itself. This method is known as proof by contrapositive. It is also distinct from the converse (If Q, then P) and the inverse (If not P, then not Q), neither of which are logically equivalent to the original conditional statement.