The Ultimate Logical nor Dog Breeds Information Guide and Reference

This article is about logical nor. For the legendary eponymous king of Norway see Nór.

Logical nor (not or) or Webb-operation is a boolean logic operator which produces a result that is the inverse of logical or. That is, p nor q is only true when neither p nor q is true, and is false otherwise. A common means of writing p NOR q is $\overline{p + q}$ , where the symbol $+$ signifies OR and the line over the expression signifies not, the logical negation of that expression

The two-input logical NOR operator is commonly described by a truth table, describing the output state for all possible input combinations:

A	B	A nor B
F	F	T
F	T	F
T	F	F
T	T	F

Nor has the interesting feature that all other logical operators can be expressed by various functions of nor.

"not p" is equivalent to "p NOR p"	$\overline{p} \equiv \overline{p + p}$
"p and q" is equivalent to "(p NOR p) NOR (q NOR q)"	$p \cdot q \equiv \overline{\overline{(p + p)} + \overline{(q + q)}}$
"p or q" is equivalent to "(p NOR q) NOR (p NOR q)"	$p + q \equiv \overline{\overline{(p + q)} + \overline{(p + q)}}$
p implies q" is equivalent to "((p NOR q) NOR q) NOR ((p NOR q) NOR q)"	$p \rightarrow q \equiv \overline{\overline{(\overline{(p+q)} + q)}+\overline{(\overline{(p + q)} + q)}}$

This is similar to the logical nand operator.