   Chapter 1.2, Problem 28E

Chapter
Section
Textbook Problem
1 views

# Let f :   Α → Β , where Α and Β are nonempty. Prove that f has the property that f ( f − 1 ( T ) )   =   T for every subset T of Β if and only if f is onto. (Compare with Exercise 15c.)Exercise 15c.c. For this same f and T = { 4 ,   9 } , show that f ( f − 1 ( T ) )   ≠   T .

To determine

To prove: f has the property that f(f1(T))=T for every subset T of B if and only if f is onto.

Explanation

Given information:

Let f:AB, where A and B are non-empty.

Proof:

Let f:AB, where A and B are non-empty.

Assume that f(f1(T))=T;TB

Let x be any element of set B.

Let T={x}

f(f1({x}))={x}

In other words, there exist aA such that f(a)=x

Since xB be any arbitrary element, there exists aA such that f(a)=x

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 