Symbols:Symbolic Logic

And

 * $\land$

And. A binary operation on two propositions.

$P \land Q$ means $P$ is true and $Q$ is also true.

Some $\LaTeX$ compilers allow  (the version of MathJax used on  does not).

In the context of propositional logic, on   is standard.

See Vector Algebra: Deprecated Symbols and Group Theory for alternative definitions of this symbol.

Or

 * $\lor$

Or. A binary operation on two propositions.

$P \lor Q$ means either $P$ is true or $Q$ is true, or both.

Its technical term is vel.

Some $\LaTeX$ compilers allow  (the MathJax used on  does not).

In the context of propositional logic, on   is standard.

Not

 * $\neg$

Not. A unary operator on a propositions.

$\neg Q$ means not $Q$, the logical opposite (negation) of $Q$.

The effect of the unary operator $\neg$ is to reverse the truth value of the statement following it.

Nand

 * $\uparrow$

Logical Nand. A binary operation on two propositions.

$P \uparrow Q$ means not $P$ and $Q$ together.

The symbol is named the Sheffer stroke, after Henry Sheffer.

Nor

 * $\downarrow$

Logical Nor. A binary operation on two propositions.

$P \downarrow Q$ means neither $P$ nor $Q$.

The symbol is named the Quine arrow, after Willard Quine.

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

See Arithmetic and Algebra, Vector Algebra and Abstract Algebra for alternative definitions of this symbol.



Called ampersand.

In MediaWiki $\LaTeX$, its code is.

Or


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.

See Arithmetic and Algebra, Vector Algebra and Group Theory for alternative definitions of this symbol.

Not


Not. A binary operation on two propositions.

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

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

See Arithmetic and Algebra and Set Operations and Relations for alternative definitions of this symbol.


 * $\sim$

The symbol $\sim$ is also sometimes used for Not.

Nand

 * $\mid$

Logical Nand. A binary operation on two propositions.

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

This is also sometimes referred to as the Sheffer stroke.


 * $p \bar \curlywedge q$

This is derived from the symbol used by Charles Sanders Peirce to denote the Logical Nor, sometimes called the ampheck.

Nor

 * $\curlywedge$

Logical Nor. A binary operation on two propositions.

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

This is the symbol used by Charles Sanders Peirce to denote the Logical Nor, and is sometimes called the ampheck.

The usual ways of expressing neither $p$ nor $q$ nowadays are:
 * $\neg \left({p \lor q}\right)$


 * $\overline {p \lor q}$


 * $p \downarrow q$