Contraposition Totally Explained

Everything about Contraposition totally explained

ť For contraposition in the field of traditional logic, see Contraposition (traditional logic).

Contraposition is a logical relationship between two propositions of material implication. One proposition is the contrapositive of the other just when its antecedent is the negated consequent of the other, and vice-versa, resulting in two statements that are logically equivalent. Strictly, a contraposition can only exist between two statements each of which is no more complex than involving the same two propositions materially implicated. However, it's common to see two statements called contrapositives just when the statements each contain a material conditional, and are precisely the same apart from one of these implications being the contrapositive of the other (in the strict sense).
In propositional logic, a proposition Q is materially implicated by a proposition P when the following relationship holds:
ť

(P 	o Q)

In vernacular terms, this states "If P then Q". The contrapositive of this statement would be:
ť

(
eg Q 	o 
eg P)

That is, "If not-Q then not-P", or more clearly, "If Q isn't the case, then P isn't the case." The two above statements are said to be contraposed. Due to their logical equivalence, stating one is effectively the same as stating the other, and where one is true, the other is also true (likewise with falsity). Any propositions containing the first statement (for example

forall

isn't a rational number.

Further Information

Get more info on 'Contraposition'.

External Link Exchanges

Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:

<a href="http://contraposition.totallyexplained.com">Contraposition Totally Explained</a>

Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned.