Exclusive disjunction (aut)

Alongside the Latin “vel” (the inclusive OR, which also admits the case of both being true) there exists a second “or”: the “aut”, which excludes the case in which both are true.

Example — Exclusive "aut" (XOR)

The exclusive disjunction, ”$p$ or $q$ but not both”, is denoted $p\veebar q$ and has the following table: $(V,V)\to F,\quad (V,F)\to V,\quad (F,V)\to V,\quad (F,F)\to F.$ It is the Latin “aut”, contrasted with “vel”. We shall meet it again, in the form of a set, in the symmetric difference $A\triangle B$.

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Topics: Set theory
Concepts: Disjunction · Exclusive disjunction