Question

Show that an onto function f : {1, 2, 3} → {1, 2, 3} is always one-one.​

Answer 1

Solution :Suppose f is not one-one. Then there exists two elements, say 1 and 2 in thedomain whose image in the co-domain is same. Also, the image of 3 under f can beonly one element. Therefore, the range set can have at the most two elements of theco-domain {1, 2, 3}, showing that f is not onto, a contradiction. Hence, f must be one-one.