---
tag: 4EZWY60NYT
kind: concept
name: Material nonimplication
aliases: [abjunction]
sources:
  - wikipedia: en:11880982@r1374749453
    locator: Material nonimplication
    note: adopted
    mention: wikipedia://en/11880982
    sections: [Summary]
same_as:
  wikidata: Q427343
  wikipedia: Material nonimplication
inventory: [BC307CYVQQ]
---

## Summary

**Material nonimplication** or **abjunction** (la) is a term referring to a logic operation used in generic circuits and Boolean algebra. It is the [[negation|029JBBF693]] of [[material implication|0NMG7W7Q11]]. That is to say that for any two [[propositions|0ZGC7ZESYN]] $P$ and $Q$, the material nonimplication from $P$ to $Q$ is true if and only if the negation of the material implication from $P$ to $Q$ is true. This is more naturally stated as that the material nonimplication from $P$ to $Q$ is true only if $P$ is true and $Q$ is false.