# contrapositive

con·tra·pos·i·tive*contrapositive*of “All A is B” is “All not-B is not-A”

**MLA Style**

"contrapositive." YourDictionary, n.d. Web. 24 May 2018. <http://www.yourdictionary.com/contrapositive>.

**APA Style**

contrapositive. (n.d.). Retrieved May 24th, 2018, from http://www.yourdictionary.com/contrapositive

## contrapositive

noun

*Logic*

*All not-Y is not-X*is the contrapositive of

*All X is Y.*

**MLA Style**

"contrapositive." YourDictionary, n.d. Web. 24 May 2018. <http://www.yourdictionary.com/contrapositive>.

**APA Style**

contrapositive. (n.d.). Retrieved May 24th, 2018, from http://www.yourdictionary.com/contrapositive

## contrapositive

- From a proposition, its inverse, its converse, and its contrapositive are derived as follows:
- Proposition: "If P then Q."
- Inverse: "If not P then not Q."
- Converse: "If Q then P."
- Contrapositive: "If not Q then not P."

- If a proposition is true then its contrapositive is, too. Thus, if the statement "If I'm Roman, then I can speak Latin" is true, then it logically follows that the statement "If I can't speak Latin, then I'm not Roman" must also be true.

**MLA Style**

"contrapositive." YourDictionary, n.d. Web. 24 May 2018. <http://www.yourdictionary.com/contrapositive>.

**APA Style**

contrapositive. (n.d.). Retrieved May 24th, 2018, from http://www.yourdictionary.com/contrapositive