what is domain range and condomain of a relation.give examples
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Answer:
Step-by-step explanation:
We are familiar with the terms Domain of a Function and Range of a Function. But what does it mean? Before diving deeper into the topic, let us understand what a function is?
Functions:
Functions are one of the fundamental concepts in mathematics which have got numerous applications in the real world. Be it the mega skyscrapers or super-fast cars, and their modelling requires methodical application of functions. Almost all the real-world problems are formulated, interpreted, and solved using functions.
An understanding of relations is required in order to understand functions. And understanding of Cartesian products is required to understand relations. A Cartesian product of two sets A and B is collection of all the ordered pairs (a,b) such that a∈A and b∈B . A relation is a subset of a Cartesian product. Hence, a relation is a rule that “relates” an element from one set to an element from another set. A function is a special kind of relation. Let us consider a relation F from set A to B.
Definition 1: A relation F is said to be a function if each element in set A is associated with exactly one element in set B.
To understand the difference between relations and functions, let us take an example. Set A contains the name of all the countries that have won the cricket world cup and set B contains the list of years in which world cup was played. The arrow diagram in the fig.1 represents a relation R but not a function. This is because elements in the set A are associated with more than one element in the set B.
Domain And Range Of A Function
But if we define a relation F from the set A to B such that it associates the countries with the year in which, they won the world cup for the first time. Thus, for every element in the set A, we have exactly one association in the set B. This relation F shown in fig. 2 qualifies to be a function.
Domain And Range Of A Function
Domain and Range of a Function:
Remember that in case of a relation, the domain might not be the same as the left set in the arrow diagram. This is because the set may contain any element which doesn’t have an image in the right set. But in case of functions, the domain will always be equal to the first set. Range and Codomain of a function are defined in the same way as they are defined for relations.