# equivalence

[ih-kwiv-uh-luh ns or for 3, ee-kwuh-vey-luh ns]

- the state or fact of being equivalent; equality in value, force, significance, etc.
- an instance of this; an equivalent.
- Chemistry. the quality of having equal valence.
- Logic, Mathematics.
- Also called material implication.the relation between two propositions such that the second is not false when the first is true.
- Also called material equivalence.the relation between two propositions such that they are either both true or both false.
- the relation between two propositions such that each logically implies the other.

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- (of a logical or mathematical relationship) reflexive, symmetrical, and transitive.

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## Origin of equivalence^{}

1535–45; < Middle French < Medieval Latin aequivalentia, equivalent to Latin aequivalent- equivalent + -ia -ia; see -ence

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

## nonequivalence

- the relationship of being unequal or incomparable
- logic
- the relation between two statements only one of which can be true in any circumstances
- a function of two statements that takes the value true only when one but not both of its arguments is true
- a compound statement asserting that just one of its components is true

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Abbreviation: exclusive or

## equivalence

### equivalency

- the state of being equivalent or interchangeable
- maths logic
- the relationship between two statements, each of which implies the other
- Also called: biconditionalthe binary truth-function that takes the value true when both component sentences are true or when both are false, corresponding to English if and only if . Symbol: ≡ or ↔, as in –(p ∧ q) ≡ – p ∨ – q

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Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

## Word Origin and History for nonequivalence

## equivalence

### n.

1540s, from French équivalence, from Medieval Latin aequivalentia, from aequivalentem (see equivalent). Related: Equivalency (1530s).

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Online Etymology Dictionary, © 2010 Douglas Harper