Symbols:Logical Operators

And

$\land$

And. A binary operation on two propositions.

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

Its $\LaTeX$ code is \wedge or \land.

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

In the context of propositional logic \land is greatly preferred but rarely appears to be used. On this site \land 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.

Its $\LaTeX$ code is \vee or \lor.

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

In the context of propositional logic \lor is greatly preferred but rarely appears to be used. On this site \lor 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.

Its $\LaTeX$ code is \neg or \lnot.

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.

Its $\LaTeX$ code is \uparrow.

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.

Its $\LaTeX$ code is \downarrow.

Deprecated Symbols

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.

Its $\LaTeX$ code is \cdot.

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

$\&$

Called ampersand.

In standard $\LaTeX$, either $\LaTeX$Primer/MathChar.html math or $\LaTeX$Primer/TextSymbols.html text mode, its code is \&.

In MediaWiki $\LaTeX$, its code is \And.

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.

Its $\LaTeX$ code is +.

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 $\lnot$, which is what is usually used by logicians.

Its $\LaTeX$ code is -.

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.

Its $\LaTeX$ code is \sim.

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.

Its $\LaTeX$ code is | or \vert or \mid.

$p \bar \curlywedge q$

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

Its $\LaTeX$ code is \bar \curlywedge.

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.

Its $\LaTeX$ code is \curlywedge.

The usual ways of expressing neither $p$ nor $q$ nowadays are:

• $\neg \left({p \lor q}\right)$;

• $\overline {p \lor q}$;

• $p \downarrow q$.