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# a) Show that a partial function from .A to B can be viewed

ISBN: 9780073383095 37

## Solution for problem 78E Chapter 2.3

Discrete Mathematics and Its Applications | 7th Edition

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Problem 78E

a) Show that a partial function from $$A$$ to $$B$$ can be viewed as a function $$f^{*}$$ from $$A$$ to $$B \cup\{u\}$$, where $$u$$ is not an element of $$B$$ and

$$f^{*}(a)= \begin{cases}f(a) & \text { if } a \text { belongs to the domain } \\ & \text { of definition of } f \\ u & \text { if } f \text { is undefined at } a .\end{cases}$$

b) Using the construction in (a), find the function $$f^{*}$$ corresponding to each partial function in Exercise 77.

Equation Transcription:

{

Text Transcription:

A

B

f

cup {u}

f(x)= {_u   if f is undefined at a ^f(a)  if a belongs to the domain of definition of f

Step-by-Step Solution:

Solution:

Step 1 ;

In this problem we have to prove that the function can be viewed as a function

where u is not an element of B  and

This shows that is well defined.

For each  it shows that either  is in the domain of the definition of  or it is not.

If is in the domain of the definition then is the well defined element,

If  is not in the domain of the definition

In either case is well defined.

Step 2 of 2

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