Question

A mapping f : X → Y is one one if __________

(a) f(x1) ≠ f(x2) for all x1, x2 in X

(b) If f(x1) = f(x2) then x1 = x2 for all x1, x2 in X

(c) f(x1) = f(x2) for all x1, x2 in X

(d) None of the mentioned

I got this question in an international level competition.

I want to ask this question from Number of Functions topic in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer 1

The correct choice is (b) If f(x1) = f(x2) then x1 = x2 for all x1, x2 in X

The explanation is: In one one function every element in A should have unique image in B,thus if two image are equal this means there preimages are same.