# Symbols:Symbolic Logic/Deprecated Symbols

## Contents

## Deprecated Symbols of Symbolic Logic

This page contains symbols which may or may not be in current use, but are either non-standard in mathematics or have been superseded by their more modern variants.

Texts on logic often tend to use these symbols in preference to those used in mathematics.

However, on $\mathsf{Pr} \infty \mathsf{fWiki}$ the intention is to present a consistent style, and so these symbols are to be considered deprecated.

### And

- $\cdot$

And.

A binary operation on two propositions.

$P \cdot Q$ means **$P$ is true and $Q$ is true**.

In this usage, it is called **dot**.

An alternative to $P \land Q$, usually used by logicians.

The $\LaTeX$ code for \(P \cdot Q\) is `P \cdot Q`

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### Ampersand

- $\&$

$P \mathop \& Q$ means **$P$ is true and $Q$ is true**.

An alternative to $P \land Q$, which is what is usually used by logicians.

The $\LaTeX$ code for \(P \mathop \& Q\) is `P \mathop \& Q`

or `P \mathop \And Q`

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### Disjunction

- $+$

Or.

A binary operation on two propositions.

$P + Q$ means **either $P$ is true or $Q$ is true or both.**

An alternative to $P \lor Q$, which is what is usually used by logicians.

The $\LaTeX$ code for \(P + Q\) is `P + Q`

.

### Minus

- $-$

Not.

A unary operation on a proposition.

$-Q$ means **$Q$ is not true.**

An alternative to $\neg$, which is what is usually used by logicians.

The $\LaTeX$ code for \(-Q\) is `-Q`

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### Tilde

- $\sim$

Not.

A unary operation on a proposition.

$\sim Q$ means **$Q$ is not true.**

An alternative to $\neg$, which is what is usually used by logicians.

The $\LaTeX$ code for \(\sim Q\) is `\sim Q`

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### Sheffer Stroke

- $\mid$

A binary operation on two propositions.

$P \mid Q$ means **not both $P$ and $Q$ together**

This is known as the **Sheffer stroke**.

The $\LaTeX$ code for \(P \mid Q\) is `P \mid Q`

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### Modified Ampheck

- $P \mathop {\bar \curlywedge} Q$

A binary operation on two propositions.

$P \mathop {\bar \curlywedge} Q$ means **not both $P$ and $Q$ together**.

The $\LaTeX$ code for \(P \mathop {\bar \curlywedge} Q\) is `P \mathop {\bar \curlywedge} Q`

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### Ampheck

- $\curlywedge$

A binary operation on two propositions.

$P \curlywedge Q$ means **neither $P$ nor $Q$**.

The $\LaTeX$ code for \(P \curlywedge Q\) is `P \curlywedge Q`

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