Symbols:Symbolic Logic

And

 * $$\and$$
 * And. A binary operation on two propositions. $$P \land Q$$ means $$P$$ is true and $$Q$$ is also true.
 * Its LaTeX code is \wedge, \and or \land.

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

Or

 * $$\or$$
 * Or. A binary operation on two propositions. $$P \vee Q$$ means either $$P$$ is true or $$Q$$ is true, or both.
 * Its technical term is vel.
 * Its LaTeX code is \vee, \or or \lor.

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 or \lnot.

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 $$P \and Q$$, 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.


 * $$\And$$ 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 $$P \or Q$$, which is what is usually used by logicians.
 * Its LaTeX code is +</tt>.
 * 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.
 * Its LaTeX code is -</tt>.
 * 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:
 * $$\neg \left({p \or q}\right)$$;


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


 * $$p \downarrow q$$.