Using proof by contradiction vs proof of the contrapositive
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.
Terminology question: why "positive" in "contrapositive"?
Apr 13, 2026 · Historically, this is connected with the doctrine of contraposition in medieval logic. There, universal categorical propositions (the A and E forms in the square of opposition) were taken to …
When to use the contrapositive to prove a statment
My question tries to address the intuition or situations when using the contrapositive to prove a mathematical statement is an adequate attempt. Whenever we have a mathematical statement of the …
Contraposition of "P if and only if Q" - Mathematics Stack Exchange
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" …
Guidelines on using Proof by Contrapositive
Aug 31, 2019 · You can use a proof by contraposition whenever you have an implication to prove. A good guideline for when you maybe should use a proof by contraposition is when the negation of the …
discrete mathematics - Using proof by contraposition to show that if …
Jan 15, 2015 · I know that $2\left (2k + 2\right) + 1$ means that the number is odd and the contraposition has now be proofed. And I understand that we got to $2\left (3k+2\right)+1$, then …
Proving that the reciprocal of an irrational is irrational
The question I am working on is: Prove that if x is irrational, then 1/x is irrational. My proof differs from the one given in the answer key; but I still feel that mine is valid. Could someone
About proofs by contrapositive and proofs by contradiction
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 …
Contraposition and contradiction - Mathematics Stack Exchange
Sep 27, 2018 · @deeppinkwater (1): "Reasoning by contraposition" is a somewhat informal description of a proof strategy; it is not usually a crisp technical notion in formal proof theory.
logic - Contraposition's value is rigorous logical reasoning ...
May 25, 2021 · Is there any proof, in classical logic, for the law of contraposition that proves, using pure logical constructs, both sides of the equivalence without using double negation elimination or the law …