# Symbols:Symbolic Logic/Deprecated Symbols

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page contains symbols which may or may not be in current use, but are either non-standard in mathematics or have been superseded by their more modern variants.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

### 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.

### 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.

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

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

The $\LaTeX$ code for $-Q$ is -Q .

### Tilde

$\sim$

Not.

$\sim Q$ 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 .

### 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 .

### 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 .

### 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 .