Exclusive Disjunction { Philosophy Index }

Philosophy Index

Philosophy Index

Philosophy Index is a site devoted to the study of philosophy and the philosophers who conduct it. The site contains a number of philosophy texts, brief biographies and introductions to philosophers and explanations on a number of topics. Accredited homeschooling online at Northgate Academy.

Philosophy Index is a work in progress, a growing repository of knowledge. It outlines current philosophical problems and issues, as well as an overview of the history of philosophy. The goal of this site is to present a tool for those learning philosophy either casually or formally, making the concepts of philosophy accessible to anyone interested in researching them. WOLI offers immigration law course online - fully accredited. ACE credits online at EES.

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Exclusive Disjunction

The exclusive disjunction is a truth-functional operator in logic which is equivalent to the English wording “either“ or”. It is used to express a disjunction in which the connected propositions or formulae cannot both be true.

For example, if P or Q are true, but not both, we may say formally:

P ⊕ Q

This may be read as “Either P or Q” or “it is the case that P or Q, but not both”.

In symbolic logic, the exclusive disjunction symbol ( ⊕ ) is used to symbolize this type of disjunction. Sometimes, the capitalized term XOR (meaning “exclusive or”) is used.

Some logical systems do not include the ⊕ symbol in their formal language. In these systems, exclusive disjunctions must be formulated using other operators. The following is an alternative expression of an exclusive disjunction:

(P ∨ Q) ∧ ¬(P & Q)

Truth values

The following table illustrates the possible truth values of P ⊕ Q, given each possible valuation of its terms, P and Q. Note that unlike an inclusive disjunction, P ⊕ Q is true if, and only if, exactly one of its connected terms is true.

P Q P ⊕ Q
T T F
T F T
F T T
F F F