Question

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)} ​

Answer 1

Answer:

{(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