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# Exclusive disjunction

**Exclusive disjunction**, also known as **logical inequality** or **symmetric difference**, is an operation on two logical values, typically the values of two propositions, that produces a value of *true* just in case exactly one of its operands is true.

An exclusive disjunction of propositions and may be written in various ways. Among the most common are these:

A truth table for appears below:

The exclusive disjunction of two variables belongs to the family of minimal negation operators. Thus, we have the following equivalents:

A logical graph for is shown below:

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 is two single cells, as shown below:

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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.