   Chapter 7.1, Problem 33ES ### 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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# Student A tries to define a function g : Q → Z by the rule g ( m n ) = m − n , for all integers m and n with n ≠ 0 . Student B claims that g is not well defined. Justify student B’s claim.

To determine

Student A tries to define a function g:QZ by the rule g(mn)=mn for all integers m and n with n0. Student B claims that g is not well defined. Justify student B’s claim.

Explanation

Given information:

Consider that a student A tries to define a function g:QZ by the rule g(mn)=mn, for all integers m and n with n0. And the student B claims that g is not well defined.

Concept used:

A function g:AB is said to be well defined.

If x=y then g(x)=g(y) for every x,yA.

Calculation:

Now clearly the given function g:QZ is not well defined.

Because the fraction in domain Q has one more representations as quotients of integers.

Consider,

For 24,36Q and clearly 24=36

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