Symbols:Symbolic Logic

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.

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.

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

Not

 * $\neg$
 * Not. $\neg Q$ means not $Q$, the logical opposite (negation) of $Q$. The effect of the unary operator $\neg$ is to reverse the truth value of the following statement.

Its $\LaTeX$ code is \neg</tt> or \lnot</tt>.

Nand

 * $\uparrow$
 * Logical Nand. $P \uparrow Q$ means not $P$ and $Q$ together.

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

Its $\LaTeX$ code is \uparrow</tt>.

Nor

 * $\downarrow$
 * Logical Nor. $P \downarrow Q$ means neither $P$ nor $Q$.

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

Its $\LaTeX$ code is \downarrow</tt>.

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</tt>.

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




 * Called ampersand.

In standard $\LaTeX$, either math or text mode, its code is \&</tt>.

In MediaWiki $\LaTeX$, its code is \And</tt>.

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

Its $\LaTeX$ code is +</tt>.

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

Not

 * Not: an alternative to $\lnot$, which is what is usually used.
 * Not: an alternative to $\lnot$, which is what is usually used.

Its $\LaTeX$ code is -</tt>.

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</tt>.

Nand

 * This is also sometimes referred to as the Sheffer stroke.
 * This is also sometimes referred to as the Sheffer stroke.

Its $\LaTeX$ code is |</tt>.


 * $p \bar \curlywedge q$
 * 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</tt>.

Nor

 * $\curlywedge$
 * This is similar to the symbol used by Charles Sanders Peirce to denote the Logical Nor, and is sometimes called the ampheck.

Its $\LaTeX$ code is \curlywedge</tt>.


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


 * $\overline {p \lor q}$;


 * $p \downarrow q$.