kontrapositiotodistukseen

Kontrapositiotodistus, also known as proof by contrapositive, is a method of indirect proof used in logic and mathematics. It is based on the logical equivalence between a conditional statement and its contrapositive. A conditional statement is of the form "If P, then Q," where P is the antecedent and Q is the consequent. Its contrapositive is "If not Q, then not P." The principle of contrapositive proof states that if the contrapositive statement is true, then the original statement is also true.

To construct a proof by contrapositive, one begins by assuming the negation of the consequent (not Q). From this assumption, the goal is to logically deduce the negation of the antecedent (not P). If this deduction is successful, then the original implication (If P, then Q) has been proven. This method is particularly useful when proving statements of the form "if A implies B" where it is easier to show that if B is false, then A must also be false. For example, to prove "If x is an odd number, then x squared is an odd number," one might assume that x squared is not odd (i.e., x squared is even) and then show that x must therefore not be odd (i.e., x is even). This is a valid method because of the inherent logical relationship between a statement and its contrapositive.