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equivalent (Definition)

Two statements $ A$ and $ B$ are said to be logically equivalent (typically shortened to equivalent) when $ A$ is true if and only if $ B$ is true (that is, $ A$ implies $ B$ and $ B$ implies $ A$). This is usually written as $ A \Leftrightarrow B$. For example, for any integer $ z$, the statement “$ z$ is positive” is equivalent to “$ z$ is not negative and $ z\neq 0$”.



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"equivalent" is owned by sleske. [ full author list (2) ]
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See Also: biconditional, Heronian mean is between geometric and arithmetic mean

Also defines:  logically equivalent
Keywords:  equivalent, equivalence, formal logic
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Cross-references: integer, implies
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This is version 4 of equivalent, born on 2002-12-17, modified 2007-05-16.
Object id is 3769, canonical name is Equivalent3.
Accessed 10034 times total.

Classification:
AMS MSC: 03B05 (Mathematical logic and foundations :: General logic :: Classical propositional logic)
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