Concise Guide to Formal Methods pp 65-92 | Cite as

# Sets, Relations and Functions

## Abstract

This chapter provides an introduction to fundamental building blocks in mathematics such as sets, relations and functions. Sets are collections of well-defined objects; relations indicate relationships between members of two sets *A* and *B*; and functions are a special type of relation where there is exactly (or at most) one relationship for each element *a* ϵ *A* with an element in *B*. A set is a collection of well-defined objects that contains no duplicates. A binary relation *R* (*A*, *B*) where *A* and *B* are sets is a subset of the Cartesian product (*A* × *B*) of *A* and *B*. A total function *f*: *A* → *B* is a special relation such that for each element *a* ϵ A there is exactly one element *b* ϵ B. This is written as *f*(*a*) = *b*. A partial function differs from a total function in that the function may be undefined for one or more values of *A*.

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