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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 , 5 , 9 } and Y = { 3 , 4 , 7 } .

a. Define f : X Y by specifying that f ( 1 ) = 4 , f ( 5 ) = 7 , f ( 9 ) = 4. Is f one-to-one? Is f onto? Explain your answers.

b. Define g : X Y by specifying that g ( 1 ) = 7 , g ( 5 ) = 3 , g ( 9 ) = 4. Is g one-to-one? Is g onto? Explain your answer.

To determine

(a)

To check:

Whether f is one-to-one or onto.

Explanation

Given information:

Let X={1,5,9} and Y={3,4,7}

A function f:XY is defined by specifying that

f(1)=4,f(5)=7,f(9)=4.

Concept used:

A function is said to be one-to-one if every element in domain mapped with single element in co-domain.

A function f is said to be Onto function if and only if each element in the co-domain of f is the image of at least one element in the domain of f

To determine

(b)

To find:

Whether f is one-to-one or onto.

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