# truth tables

Published articles for truth tables.

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## Methods of Proof -- Contrapositive

DevFeed: [Methods of Proof -- Contrapositive](<https://devfeed.tech/articles/methods-of-proof-contrapositive-40304.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2013/02/22/methods-of-proof-contrapositive/>)

Published: 2013-02-22T20:43:25Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [function](<https://devfeed.tech/topics/function.md>), [functions](<https://devfeed.tech/topics/functions.md>), [object](<https://devfeed.tech/topics/object.md>)

Tags: [contrapositive](<https://devfeed.tech/tags/contrapositive.md>), [function](<https://devfeed.tech/tags/function.md>), [functions](<https://devfeed.tech/tags/functions.md>), [injective-functions](<https://devfeed.tech/tags/injective-functions.md>), [methods-of-proof](<https://devfeed.tech/tags/methods-of-proof.md>), [object](<https://devfeed.tech/tags/object.md>), [pigeonhole-principle](<https://devfeed.tech/tags/pigeonhole-principle.md>), [truth-tables](<https://devfeed.tech/tags/truth-tables.md>)

### AI overview

This post introduces the contrapositive as one of four basic proof methods and begins developing the mathematical definition of functions on sets. It explains functions as sets of ordered pairs, with each input associated with exactly one output.

### Source excerpt

In this post we'll cover the second of the "basic four" methods of proof: the contrapositive implication. We will build off our material from last time and start by defining functions on sets. Functions as Sets So far we have become comfortable with the definition of a set, but the most common way to use sets is to construct functions between them. As programmers we readily understand the nature of a function, but how can we define one mathematically?