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Inverse of a Relation

Definition: inverse of a binary relation R

R^-1 := {<b, a>: a in domain(R) /\  b in range(R) /\  <a, b> in R}.

Proposition:
The inverse of a relation from A to B is a relation from B to A.

forall R, A, B: R subset A x B => R^-1 subset B x A.

Example:

• R := {<0, 0>, <0, 1>, <0, 2>, <1, 2>}.
• R^-1 = {<0, 0>, <1, 0>, <2, 0>, <2, 1>}.