Definition:Disjunction/Disjunct

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.

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.

Some sources refer to the members of the disjunction.

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

• 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences (2nd ed.) ... (previous) ... (next): $\S \text{II}.7$: Sentential Calculus
• 1964: Donald Kalish and Richard Montague: Logic: Techniques of Formal Reasoning ... (previous) ... (next): $\text{II}$: 'AND', 'OR', 'IF AND ONLY IF': $\S 1$
• 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $3$ Conjunction and Disjunction
• 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $2$ Arguments Containing Compound Statements: $2.1$: Simple and Compound Statements
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): disjunct or alternant
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): disjunct
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): disjunct