Relations and Functions
Relations and Functions is the topic that we are going to discuss on this page.In our earlier classes, we would have already learned about sets. This topic is further reading of sets. When we associate elements from one set to another set, relation and function come in to picture. Usually, this association is called mapping.
Now, let us learn about Relations & Functions in detail.
Relations: In natural language relations are kind of relationship between two sets of information.
Usually we define relations between two sets.
For example let us think about the students in a class and their heights. One set represents the students and the other set represents their heights.
These two sets are related with the heights. The starting set(students) is called as Domain and the ending point (heights) is called as Range.
In other words, Relation is a set of ordered pairs, usually defined by some sort of rule.
Domain is the set from which the relation starts and Rangeis the set at which the relation ends.
Function: A function is a well behaved relation.
'Well behaved relation' means, for a given a starting point in the starting set(domain), we know exactly where to go in the end set(range).
All functions are relations, but not all relations are functions.
In the above example, students related with heights, the relation is not well behaved, so it is not a function.
In other words a Function is a set of ordered pairs, such that for a given element in the Domain, we have exactly only one element as a image in the Range.
In the following example, the function has been shown. The set A is called as Domain, and the set B is called as Range, and according to the definition, each element in A is related to a element in B. So it is a function.