Symbols:Symbolic Logic

"And"

 * $$\wedge$$
 * "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"

 * $$\vee$$
 * "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.

= 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</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 $$P \lor Q$$, 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>.

"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:
 * $$\lnot \left({p \lor q}\right)$$;


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


 * $$p \downarrow q$$.