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# How to Determine if a Relation is a Function?

TopFunction can be defined as a Set of Ordered Pair such that two elements present in pair should be different.
Relation: Let O and P are two Sets then relation 'R' defined from set 'O' to set 'P', is a subset of O * P. Relation is denoted in list form and in tabular form as well.

Let's discuss how to determine if a relation is a function. We will understand it with help of an example in step form:

Step 1: Suppose we have Relations:
(4, 5), (6, 10), (10, 10), (3, 4)
(0, 0), (0, 1), (1, 4), (2, 4)
(3, 2), (5, 6), (9, 5), (2, 0)
(9, 4), (9, 0), (8, 8), (5, 8)
Here we have to determine whether each relation is a function not.

Step 2: Here we will see case for each relation one by one. Function is a relation if, no two ordered pair have same first value.
So in first case: (4, 5), (6, 10), (10, 10), (3, 4).
This relation is a funciton because none of the four ordered pairs have same first element.
In case of second relation: (0, 0), (0, 1), (1, 4), (2, 4).
Given relation is not a function because first two ordered pair have same first element.
In case of third relation: (3, 2), (5, 6), (9, 5), (2, 0).
In this case given relation is a function because none of the first element in four ordered pair is same.
In last relation (9, 4), (9, 0), (8, 8), (5, 8).
It is not a function because first two ordered pair have first same element.
In this way we can determine relation is a function or not.