   Chapter 7.3, Problem 18ES ### 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 Y and Z are sets and g : Y → Z is a one-to-one function. This means that if g takes the same value on any two elements of Y, and g ( a ) = g ( b ) , then it can be inferred that a = b . What can be inferred in the following situations? s k and S m are elements of Y and g ( s k ) = g ( s m ) . z / 2 and t/2 are elements of Y and g ( z / 2 ) = g ( t / 2 ) . f ( x 1 )   and   f ( x 2 ) are elements of Y are g ( f ( x 1 ) ) = g ( f ( x 2 ) ) .

To determine

(a)

To find:

The inferred results in the given situation:

sk and sm are elements of Y and g(sk)=g(sm).

Explanation

Given information:

g:YZ is a one-to-one function.

Concept used:

A function is said to be one-to-one function if the distinct elements in domain must be mapped with distinct elements in co-domain.

Calculation:

g:YZ is a one-to-one function.

So by definition, we get:

g(sk)=

To determine

(b)

To find:

The inferred results in the given situation:

z/2 and t/2 are elements of Y and g(z/2)=g(t/2).

To determine

(c)

To find:

The inferred results in the given situation:

f(x1)and f(x2) are elements of Y and g(f(x1))=g(f(x2)).

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