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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen
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Determine whether each of the functions f(a) = a div d and

Chapter 4, Problem 47E

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QUESTION:

Determine whether each of the functions f(a) = a div d and g(a) = a mod d, where d is a fixed positive integer, from the set of integers to the set of integers, is one-to-one, and determine whether each of these functions is onto.

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QUESTION:

Determine whether each of the functions f(a) = a div d and g(a) = a mod d, where d is a fixed positive integer, from the set of integers to the set of integers, is one-to-one, and determine whether each of these functions is onto.

ANSWER:

Solution:Step 1In this problem we have to determine whether each of the functions and, from set of integers to set of integers, is one-to-one, and To determine whether each of these functions is onto, where d is fixed positive integer.If every element of the codomain is mapped to by at most one element of the domain, then function is called one-to-one.If every element of the codomain is mapped to by at least one element of the domain, then function is called onto .

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