Of course that proposition can be proved directly as well: the point is just that the proof given is genuinely a proof by contradiction, rather than a proof by contraposition.

Here contraposition is not especially helpful because the specific choice f = g f = g gives either direction. That is, 3 (a) has infinitely many hypotheses, but one of them is sufficient to deduce the conclusion. …

Feb 7, 2017 · I'm understanding the basic idea of contraposition, when it comes to propositional logic and writing proofs, but I'm having trouble figuring out what the contraposition of "P if and only if Q" …

Aug 6, 2018 · Remark. Both proofs by contraposition and proofs by contradiction are valid in classical logic, but in general they are not valid in intuitionistic logic (roughly speaking, a constructive logic that …

Direct proof of a contraposition Ask Question Asked 12 years ago Modified 12 years ago

Jul 25, 2016 · Edit: I should mention that your setup can still show that the contrapositive is equivalent (see JMoravitz's answer). You just have to stay consistent with your setup: the set P P denotes all …

Jul 13, 2015 · I wanted to ask (as the title suggests) why the law of contraposition is a tautology. My book states that a tautology is a statement which is true for the all the values of the variables included.

We may be interested by Kripke models of intuitionistic logic. Finding a Kripke model in which the second formula is satisfied but not the first one, proves (using the completeness theorem) that you …

Jul 30, 2020 · Contraposition on the implication inside the statement is a special case of proof by contradiction where one assumes ¬Q ¬ Q and P P, derives a contradiction (not necessarily to P P …

Nov 21, 2023 · Proof of contraposition theorem using logical (semantic) entailment definition Ask Question Asked 2 years, 1 month ago Modified 2 years, 1 month ago