   Chapter 7.2, Problem 29ES ### 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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# Define H : R × R → R × R as follows: H ( x , y ) = ( x + 1 , 2 − y ) for every ( x , y ) ∈ R × R . Is H one-to-one? Prove or gives a counterexample. Is H onto? Prove or give a counterexample.

To determine

(a)

To check:

Whether H is one-to-one or not.

Explanation

Given information:

A function H:×× is defined as follows,

H(x,y)=(x+1,2y) for all (x,y)×.

Concept used:

In one-to-one function, distinct elements in domain are mapped with distinct elements in co-domain.

Calculation:

Suppose (x1,y1) and (x2,y2) are any element of × such that

H(x1,y1)=H(x2,y2) [We must show that (x1,y1

To determine

(b)

To check:

Whether H is onto or not.

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