Question

1. State whether the following relations are functions or not. If it is a function check for one-tooneness and ontoness. If it is not a function, state why? (i) If A = {a, b, c} and f = {(a, c), (b, c), (c, b)}; (f : A → A). (ii) If X = {x, y, z} and f = {(x, y),(x, z),(z, x)}; (f : X → X).

Answer 1

Answer:

A function is a set of ordered pairs in which each x-element has only ONE y-element associated with it.

Since no two-ordered pairs have same first first component, it is a function .