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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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Let X = { 1 , 3 , 5 } and Y = { a , b , c , d } . Define g : X Y by the following arrow diagram.

Chapter 7.1, Problem 2ES, Let X={1,3,5} and Y={a,b,c,d}. Define g:XY by the following arrow diagram. What the domain of g and

  1. What the domain of g and the co-domain of g.
  2. Find g ( 1 ) , g ( 3 ) , and g ( 5 ) ?
  3. What is the range of g?
  4. Is 3 an inverse image of a? Is 1 an inverse image of b?
  5. What is the inverse image of b? of c?
  6. Represent g as a set of ordered pairs.

To determine

(a)

Write the domain of g and the co-domain of g.

Explanation

Given information:

Concept used:

f(x)=yHere, x:domainy:codomain

Calculation:

Consider the following sets as,

X={1,3,5} and Y={a,b,c,d}.

Also, a function g:XY defined as follows.

The definition for domain, Codomain and range of a function are as follows:

Domain: The domain of a function g(x) is the set of all values for which the function is defined

To determine

(b)

Find g(1),g(3) and g(5).

To determine

(c)

What is the range of g

To determine

(d)

Is 3 an inverse image of a ? Is 1 an inverse image of b ?

To determine

(e)

What is the inverse image of b ? Of c ?

To determine

(f)

Represent g as a set of ordered pairs.

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