Definition:Disjunction/Disjunct

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Definition

Let $p \lor q$ be a compound statement whose main connective is the disjunction:

$p \lor q$ if and only if $p$ is true or $q$ is true or both are true.


The substatements $p$ and $q$ are known as the disjuncts, or the members of the disjunction.


Also known as

A disjunct can also been seen referred to as

  • an alternant or alternative, particularly where a disjunction is referred to as a (logical) alternation
  • a summand, particularly where a disjunction is referred to as a (logical) sum.


Linguistic Note

The word alternative, as a synonym for disjunct, is the usual word used in natural language (specifically English) to mean one of two options.


It is technically incorrect to use the word alternative when there are more than two options:

The way I see it, we have three alternatives ...

To be rigorously correct here, one needs to use the word choices instead of alternatives.


Sources