Discrete Mathematics

Question

Let A and B be subsets of the set S, where S = 10 and B = 5. Let f: A → B

be a function.

(a) If f is one-to-one, what are the possible values of A?

(b) If f is onto, what are the possible values of A?

(c) If f is a bijection, what are the possible values of A?

Answer 1

a) 1-1 means each value in A must have a unique value in B, so |A| <= 5

b) onto means each value in B must be mapped to by a value in A, so |A| >= 5

c) If it is bijective, it must be 1-1 and onto, so |A| <= 5 and |A| >= 5, so |A| = 5