# Definition:Logical Connective/Binary

< Definition:Logical Connective(Redirected from Definition:Binary Logical Connective)

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## Definition

A **binary logical connective** (or **two-place connective**) is a logical connective whose effect on its compound statement is determined by the truth value of *two* substatements.

In standard Aristotelian logic, there are 16 **binary logical connectives**, cf. Binary Truth Functions.

In the field of symbolic logic, the following four (symbols for) **binary logical connectives** are commonly used:

- Conjunction: the
**And**connective $p \land q$:**$p$ is true**.*and*$q$ is true

- Disjunction: the
**Or**connective $p \lor q$:**$p$ is true**.*or*$q$ is true,*or possibly both*

- The conditional connective $p \implies q$:
.*If*$p$ is true,*then*$q$ is true

- The biconditional connective $p \iff q$:
**$p$ is true**, or*if and only if*$q$ is true**$p$**.*is equivalent to*$q$

## Also defined as

Some sources use the term **logical connective** to mean **binary logical connective** exclusively, on the grounds that a **unary logical connective** does not actually "connect" anything.

However, this is a trivial distinction which can serve only to confuse.

## Also known as

A **binary logical connective** is also known as:

Some sources just call it a **binary connective**.

## Also see

- Results about
**logical connectives**can be found**here**.

## Sources

- 1980: D.J. O'Connor and Betty Powell:
*Elementary Logic*... (previous) ... (next): $\S \text{I}: 2$: Logical Constants $(1)$ - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**connective** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**connective**