Exercise 10, § 3

Let A, B, C be sets, $f$ a mapping of A into B, $g$ a mapping of B into C, $h$ a mapping of C into A. Show that if two of the three mappings $h \circ g \circ f$, $g \circ f \circ h$, $f \circ h \circ g$ are surjections and the third is an injection, then $f$, $g$, $h$ are all bijections.