How exclusive is your or?

An operation shared by Boolean algebras such as propositional logic, switching theory, conditional statements in programming, and computer logic design is the 'exclusive or'.  It also occurs in set theory and geometric modeling as 'symmetric difference'. It is defined as x + y = (x v y) ^ ~(x ^ y) = (x v y) ^ (~x v ~y) and is usually represented by a plus sign inside a circle, but to avoid the need for a formula-drawing editor, it will be represented as a plus sign, '+'.
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This theory is all set(s)

Set theory is, along with geometry, arithmetic and algebra, one of the major foundations of mathematics.  It is described by multi-valued (possibly infinitely-valued) Boolean algebras.

A set is a collection of things (objects, abstractions, other sets, etc.).  The things that make up a set are called members or elements of that set.  The set which consists of all things that may be members of the sets being considered is called the universe of discourse.

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