   Chapter 7.2, Problem 12ES ### 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
1 views

# a. Define F : Z → Z   by the rule F ( n ) = 2 − 3 n for each integer n. (i) Is F one-to-one? Prove or give a counterexample. (ii) Is F onto? Prove or give a counterexample. b. Define G   :   R   →   R by the rule G ( x )   =   2 − 3 x for each real number x. Is G onto? Prove or give a counterexample.

To determine

(a)

To prove F is one-to-one and onto otherwise give counterexample.

Explanation

Given information:

Define F:ZZ by the rule, F(n)=23n for all integers n.

Calculation:

Let us suppose x,yZ and assume that F(x)=F(y) now for proving one-to-one x=y must be shown.

So from the definition of F(n), the expression can be written as follows-

23x=23y3x=3y{Subtracting 2 on both sides}x=y

To determine

(b)

To prove G is onto otherwise give counterexample.

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