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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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Define Floor: R Z by the formula Floor ( x ) = x , for every real number x.

  1. 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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