Suppose F: X Y is one-to-one. a. Prove that for all subsets A X, F1(F(A)) = A. b. Prove

Chapter 7, Problem 40

(choose chapter or problem)

Suppose \(F: X \rightarrow Y\) is one-to-one.

a. Prove that for all subsets \(A \subseteq X, \quad F^{-1}(F(A))=A\).

b. Prove that for all subsets \(A_{1}\) and \(A_{2}\) in X, \(F\left(A_{1} \cap A_{2}\right)=F\left(A_{1}\right) \cap F\left(A_{2}\right)\).

Text Transcription:

F: X rightarrow Y

A subseteq X, quad F^-1 (F(A))=A

A_1

A_2

F(A_1 cap A_2)=F(A_1) cap F(A_2)