# Necessary and sufficient conditions

conditional or implicational relationship between two statements: a necessary condition is one which must be present in order for another condition to occur, while a sufficient condition is one which produces the said condition

In science, the terms necessary and sufficient are often used. Some conditions are necessary, meaning that they are needed for something to happen. while others are sufficient, meaning that they are enough to make something happen.

Being in the purple region is sufficient for being in A, but not necessary. Being in A is necessary for being in the purple region, but not sufficient. Being in A and being in B is necessary and sufficient for being in the purple region.
Feeding a hamster with hay is sufficient. It is however not necessary: The hamster can also be fed with carrots, to reach the same result.

## Necessity

In logic, a necessary condition for a logical statement is a logical consequence of the statement, in the sense that if statement is true, then the condition must have held.[1]

## Sufficiency

A sufficient condition for a statement is a logical precursor of the statement, in the sense that if the condition is true, then so will the statement.[1]

## Mixed use of necessity and sufficiency

Generally, a sufficient condition for a statement needs not be a necessary condition for the same statement (and vice versa). This means that some sufficient conditions are not necessary, and that some necessary conditions are not sufficient.[2]

In logic, the term if and only if (shortened to iff) is often used to describe a condition that is both necessary and sufficient.[1]

Australian philosopher John Leslie Mackie introduced the term INUS condition. INUS stands for "insufficient, but necessary part of an unnecessary but sufficient condition".[3]

## References

1. "The Definitive Glossary of Higher Mathematical Jargon". Math Vault. 2019-08-01. Retrieved 2020-10-08.
2. Swartz, Norman. "The Concepts of Necessary Conditions and Sufficient Conditions". sfu.ca. Retrieved October 8, 2020.
3. Brennan, Andrew (2017). Zalta, Edward N. (ed.). The Stanford Encyclopedia of Philosophy (Summer 2017 ed.). Metaphysics Research Lab, Stanford University.