Question

State whether the following relations are functions or not. If it is a function check for one-to-oneness and ontoness. If it is not a function, state why?

If X = {x, y, z} and f = {(x, y), (x, z), (z, x)}; (f : X → X)

Answer 1

X = {x, y, z}

f = {(x, y), (x, z), (z, x)} f : X → X

The relation f : X → X is not a function since the element x in the domain has two images in the co-domain.