Examine each of the following relations given below and state in each case, giving reasons whether it is a function or not?
i) `R={(2,1),(3,1),(4,2)}`
ii) `R={(2,2),(2,4),(3,3),(4,4)}`
iii) `R={(1,2) ,(2,3),(3,4),(4,5),(5,6),(6,7)}`

Explanation

i) Since `2,3,4` are the elements of domain of `R` having their unique images, this relation, `R` is a function.

ii) Since the same first element 2 corresponds to two different images 2 and 4, this relation is not a function.

iii) Since,every element has one and only.one image, this relation is a function.