Symbols:Symbolic Logic

"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 \lor.

"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 or \land.

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

"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.

Another symbol for "Not" is "~"

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.

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

"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": 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.

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".

The usual ways of expressing "neither $$p$$ nor $$q$$" nowadays are:
 * $$\lnot \left({p \lor q}\right)$$;
 * $$\overline {p \lor q}$$;
 * $$p \downarrow q$$.

Its LaTeX code is \curlywedge</tt>.