Inverse relation

From Wikinfo

In logic and mathematics, the inverse relation of a binary relation <math>L \subseteq X \times Y</math> is the binary relation <math>L^{-1} \subseteq Y \times X</math> defined by <math>L^{-1} = \{(y, x) : (x, y) \in L\}</math>.

The inverse relation is also called the converse relation and may be written as <math>L^{C}\!</math>, <math>L^{T}\!</math>, or <math>\breve{L}</math>.

In particular, the inverse relation of a function <math>f : X \to Y</math> is the binary relation <math>f^{-1} \subseteq Y \times X</math> defined by <math>f^{-1} = \{(y, x) : y = f(x) \}</math>. The inverse relation of a function is not necessarily itself a function. In the case that it is, it may be called the inverse function of the function in question.

See also

• Bijection
• Binary relation
• Function (mathematics)
• Inverse function
• Relation (mathematics)

References

• Adapted from the Wikipedia article, "Inverse_relation" http://en.wikipedia.org/wiki/Inverse_relation, used under the GNU Free Documentation License