Discrete mathematics

Question

Let A and B be subsets of the setS,where|S|=10and|B|=5. Letf :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

If f is 1-1 then the cardinality of the set A can not be greater than the cardinality of the set B which is 5.

If f is onto then the cardinality of A can not be smaller than the cardinality of the set B which 5.

If f is a bijection then the cardinality of the set A must be the same as the cardinality of the set B which is 5.