Abstract Algebra: Theory and Applications · Problem 1.22

Preliminaries — Thomas Judson

Mathematics — Abstract Algebra · functions-bijections-cardinality

Problem

Let

f: A \to B

and

g : B \to C

be maps. ((a)) If

g \circ f

is one-to-one, show that

f

is one-to-one. ((b)) If

g \circ f

is onto, show that

g

is onto. ((c)) If

g \circ f

is bijective, show that

f

is one-to-one and

g

is onto.