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Logical nor - Definition and Overview |
| Related Words: Balanced, Binding, Cogent, Coherent, Commonsense, Consistent, Cool, Credible, Deductive, Good, Inductive, Intelligent, Just, Legal, Legitimate, Philosophical, Pragmatic, Proper |
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- This article is about logical nor. For the legendary eponymous king of Norway see Nór.
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:
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Example Usage of Logical |
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dkimerling: The Logical conclusion of getting the best parking spot: I am at school way too early. |
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FloMaiberger: That leads me to a Logical statement that I have no need for CDs or Radio 'cause I have all songs saved on my minddisk. |
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Tov3y: Seriously, what is the point of a hiccup? I can think of Logical explanations for yawning, coughing, sneezing. Hiccups... not a chance. |
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