1 What can you say about this situation There are 3 finite s

1. What can you say about this situation?

There are 3 finite sets, A,B, and C. There are fuctions

f: A-> B which is one to one and,

g: B->C which is onto adn h: C-.A

1)what can you say about the composition of g with f?

2)how does the cardinality of c compare with that of A?

3)is there anything you can say about the long range behaviour of h composed with g composed with f applied repeatedly?

1) We can say that the composition will be one to one.

2) Since C is one to one with A we can say that both has the same number of elements, therefore their cardinality is the same.

3). We can say that it will be one to one. Since the compositions of one to one functions is an one to one function.