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.
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 …
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 …
What's the difference between a contrapositive statement and a ...
A contrapositive has truth value equivalent to the original statement: $$\text {It is raining}\implies\text {I have an umbrella}$$ has a contrapositive (and is equivalent to) $$\text {I …
predicate logic - Equivalence of contrapositive and contradiction ...
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 …
logic - How is the law of contraposition a tautology?
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 …
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 …
Contrapositive: $\forall\; n - Mathematics Stack Exchange
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prove that if $5| n^2$ then $5|n$ by contraposition
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 …
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