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# Logical NAND

**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:

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:

## Resources

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