# 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**.

## 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**