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Logical NAND

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Logical NAND (“Not And”) is an operation on two logical values, typically the values of two propositions, that produces a value of false if and only if both of its operands are true.  In other words, it produces a value of true if and only if at least one of its operands is false.

A logical NAND of propositions and may be written in various ways.  Among the most common are these:

A truth table for appears below:



A logical graph for is drawn as two letters attached to the free node of a rooted edge:

Logical Graph (PQ).jpg

The traversal string of this graph is   The proposition may be taken as a Boolean function having the abstract type where is interpreted in such a way that means and means

A Venn diagram for indicates the region where is true by means of a distinctive color or shading.  In this case the region consists of three adjacent cells, as shown below:

Venn Diagram P ⊼ Q 2.0.jpg

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Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.