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, which is an elision which evolved via an interesting linguistic process from and per se and, meaning and (the symbol $\&$) intrinsically (is the word) and.

The symbol $\&$ itself evolved from the Latin et (for and).

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

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

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.

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

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

Nand

 * $\mid$

Logical Nand. A binary operation on two propositions.

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

This is also sometimes referred to as the Sheffer stroke.


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

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

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

The usual ways of expressing not both $P$ and $Q$ together nowadays are:
 * $\neg \left({P \land Q}\right)$


 * $\overline {P \land Q}$


 * $P \uparrow Q$

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:
 * $\neg \left({P \lor Q}\right)$


 * $\overline {P \lor Q}$


 * $P \downarrow Q$