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 (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</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:
 * $\neg \left({p \lor q}\right)$;


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


 * $p \downarrow q$.