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.

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 …

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" …

Jul 30, 2020 · Proof by contraposition on the implication is an instance of proof by contradiction, but it is not identical to proof by contradiction on the universal statement. They are different proofs on …

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 …

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 …

Prove directly, by contradiction, or contraposition? If the product of two integers is even, at least one of them must be even.

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 …

Mar 26, 2016 · I just wanted to make sure that my logic here is not faulty. Up till now I've generally avoided contraposition proofs and worked only with contradiction (since we may rephrase the former …

May 12, 2015 · This is a proof by contradiction, not by contraposition. You don't assume anything false and prove it directly when you prove something by contraposition. And in fact your proof would be a …