Definition of Contrapositive. Meaning of Contrapositive. Synonyms of Contrapositive

- its logically equivalent contrapositive, and an ****ociated proof method known as § Proof by contrapositive. The contrapositive of a statement has its antecedent...
- application of the general truth that if a statement is true, then so is its contrapositive. The form shows that inference from P implies Q to the negation of Q...
- make the immediate inference that "All non-P are non-S" which is the contrapositive of the given statement. Given a type O statement, "Some S are not P...
- {\displaystyle \neg P\rightarrow \neg Q} . Since an inverse is the contrapositive of the converse, inverse and converse are logically equivalent to each...
- a\neq b,} then f ( a ) ≠ f ( b ) {\displaystyle f(a)\neq f(b)} in the contrapositive statement. Symbolically, ∀ a , b ∈ X , f ( a ) = f ( b ) ⇒ a = b , {\displaystyle...
- A^{c}.} (this follows from the equivalence of a conditional with its contrapositive). Involution or double complement law: ( A c ) c = A . {\displaystyle...
- Name Statement Contrapositive / Obverted Contrapositive Contrapositive per accidens / Obverted Contrapositive per accidens / Condition of Validity A All...
- this also has the ∀ ∃ {\displaystyle \forall \exists } -property. The contrapositive of the form with negation is constructively even weaker but it is only...
- probabilities equalling 0 {\displaystyle 0} classically entails the following contrapositive form of the above: ( ¬ B ∨ ¬ ( B → A ) ) ↔ ( ¬ A ∨ ¬ ( A → B ) ) {\displaystyle...
- the integral test for convergence. The test is typically proven in contrapositive form: If ∑ n = 1 ∞ a n {\displaystyle \sum _{n=1}^{\infty }a_{n}} converges...