Which relation is a function? { (0, 2), (0, 4), (0, 6), (0, 8) } { (1, 2), (2, 3), (3, 4), (4, 5) } { (1, 2), (2, 1), (1, 3), (3, 1) } { (1, 2), (3, 4), (5, 6), (1, 8) }

{ (1,2), (2,3), (3,4), (4,5) }

Step-by-step explanation:

A function is any relationship which takes one element of one set and assigns to it one and only one element of the second set.

From the above definition, the relation { (0,2), (0,4), (0,6), (0,8) } is not a function. 0 gives different values, if x=0, it gives 2 or 4 or 6 or 8. It is one-to-many relation

The relation { (1,2), (2,1), (1,3), (3,1) } is not a function, 1 is assigned to 2 or 3.

If x=1, it gives 2 or 3

The relation { (1,2), (3,4), (5,6), (1,8) } is not a function. It is a one - to - many relation. If x=1, it gives 2 or 8

The relation { (1,2), (2,3), (3,4), (4,5) } is a one - to - one relation and it is a function. One and only one value is assigned to only one value of the second set. It is like the function f (x) = x+1

If x=1, f (x) = 2

If x=2, f (x) = 3

If x=3, f (x) = 4

If x=4, f (x) = 5