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Exclusive disjunction

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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:

Logical Graph (P,Q).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 is two single cells, as shown below:

Venn Diagram P + Q 2.0.jpg


Document history

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.