PlanetMath (more info)
 Math for the people, by the people. Sponsor PlanetMath
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
Owner confidence rating: Medium Entry average rating: No information on entry rating
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 $z\neq 0$ '.




Anyone with an account can edit this entry. Please help improve it!

"equivalent" is owned by sleske. [ full author list (2) ]
(view preamble | get metadata)

View style:

See Also: biconditional, Heronian mean is between geometric and arithmetic mean

Also defines:  logically equivalent
Keywords:  equivalent, equivalence, formal logic
Log in to rate this entry.
(view current ratings)

Cross-references: integer, implies
There are 55 references to this entry.

This is version 4 of equivalent, born on 2002-12-17, modified 2007-05-16.
Object id is 3769, canonical name is Equivalent3.
Accessed 13096 times total.

Classification:
AMS MSC03B05 (Mathematical logic and foundations :: General logic :: Classical propositional logic)

Pending Errata and Addenda
None.
[ View all 2 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)