Logical nor
Logical nor (not or) 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 <math>\overline{p + q}<math>, where the symbol <math>+<math> signifies OR and the line over the expression signifies not, the logical negation of that expression
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"
| <math>\overline{p} \equiv \overline{p + p}<math>
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| "p and q" is equivalent to "(p NOR p) NOR (q NOR q)"
| <math>p \cdot q \equiv \overline{\overline{(p + p)} + \overline{(q + q)}}<math>
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| "p or q" is equivalent to "(p NOR q) NOR (p NOR q)"
| <math>p + q \equiv \overline{\overline{(p + q)} + \overline{(p + q)}}<math>
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| p implies q" is equivalent to "((p NOR q) NOR q) NOR ((p NOR q) NOR q)"
| <math>p \rightarrow q \equiv \overline{\overline{(\overline{(p+q)} + q)}+\overline{(\overline{(p + q)} + q)}}<math>
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This is similar to the logical nand operator.
See also:
