Abstract Algebra: Theory and Applications · Problem 1.7

Preliminaries — Thomas Judson

Mathematics — Abstract Algebra · functions-mappings

Problem

Prove part (2) of Theorem 1.2.15: If

f : A \to B

and

g : B \to C

are both one-to-one, then the mapping

g \circ f : A \to C

is one-to-one.