Question

Describe difference between relation and function

Answer 1

Hint: The distinction between relations and functions may be perplexing since they are so closely related. We need thorough knowledge and comprehension of connections and functions to distinguish between them.
The relation is known in mathematics as a collection of ordered pairs containing an entity from one set to the other. Meanwhile, function is the relationship that connects a set of inputs to a set of outputs.

Complete step-by-step answer:
Relation: A connection having a link between two or more sets of values. Alternatively, it can also be a subset of the Cartesian product. The Cartesian product \[L \times M\] between two sets \[L\] and \[M\] is the set of all possible ordered pairs with first element from \[L\] and second element from \[M\] .
For example, if \[X\] and \[Y\] are two sets, and ‘ \[a\] ' is an object from set \[X\] and ‘ \[b\] ' is an object from set \[Y\] , we can say that the objects are related if the ordered pairs \[(a,b)\] are related.
Relation is denoted by “ \[R\] ”. Example –
 \[R = \{ (5,x),(10,y),(5,z)\} \] is a relation as \[5\] is input for both \[x\] and \[z\] .
Function: A function is a relationship in which each input has only one output. It is denoted by “ \[F\] ” or “ \[f\] ”. Examples of a function:
 \[F = \{ (5,b),(10,c),(15,d)\} \]
 \[f(x) = 5x + 25\]
A function assigns unique value to every finite sequence of arguments.
Hence, we can summarize the difference between them as:
Functions are relations that bind one set of inputs to another set of outputs, while relations are a group of ordered pairs from one set of objects to another set of objects.

Note: All functions are relations but all relations are not functions.
There are eight different types of relation: Empty, Universal, Identity, Inverse, Reflexive, Symmetric, Transitive and Equivalence. They all show the relations between the sets.
A function can have following relationships:
I.One-to-one
II.Many-to-One