MathDB

Set

Source: 17-th Iranian Mathematical Olympiad 1999/2000

December 14, 2005

functionalgebra proposedalgebra

Problem Statement

Let

A

and

B

be arbitrary finite sets and let

f: A\longrightarrow B

and

g: B\longrightarrow A

be functions such that

g

is not onto. Prove that there is a subset

S

A

such that

\frac{A}{S}=g(\frac{B}{f(S)})