   Chapter 7.2, Problem 20ES ### 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 Floor: R → Z by the formula Floor ( x ) = ⌊ x ⌋ , for every real number x. Is Floor one-to-one? Prove or give a counterexample. Id Floor onto? Prove or give a counterexample.

To determine

(a)

To check:

Whether Floor is one-to-one or not.

Explanation

Given information:

The function Floor: is defined as Floor(x)=x for x.

It is the greatest integer less than or equal to the number.

x=n where xn<x+1

Concept used:

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

Calculation:

In a one-to-one function, no two or more elements of the domain map with the same element of the co-domain.

Let the elements of the domain, to be analyzed, are two positive integers x1 and x2

To determine

(b)

To check:

Whether Floor is onto or not.

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