   Chapter 7.2, Problem 41ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Suppose F : X → Y is into. Prove that for every subset B ⊆ Y , F ( F − 1 ( B ) ) = B .

To determine

To Prove:

If F:XY is onto function, then F(F1(B))=B for any subset BY.

Explanation

Given information:

Given that F:XY is onto

Concept used:

Onto: Every element in codomain must be mapped with the element in domain.

Proof:

Let BY

We need to show this by two parts

(i)F(F 1(B))B(ii)F(F 1(B))B

First we have to prove F(F1(B))B

Let xF(F1(B))

By the definition of image set

x=F(y)for someyF1(B)

By the definition of inverse image set

F(y)B

Therefore x=F(y)B

xB

Hence, we have

F(F1(B))B

Let yB

Since BY and F is onto

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