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# Logical nor

(Redirected from Nor)

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.