   Chapter 7.2, Problem 30ES ### 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 J = Q × Q → R by the rule J ( r , s ) = r + 2 s for each ( r , s )   ∈ Q × Q . Is J one-to-one? Prove or give a counterexample. Is J onto? Prove or give a counterexample.

To determine

(a)

To check:

Whether J is one-to-one or not.

Explanation

Given information:

J:× is defined by the rule J(r,s)=r+2s for all (r,s)×.

Concept used:

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

Calculation:

To verify that J is one-to-one suppose J(r1,s1)=J(r2,s2).

J(r1,s1)=J(r2,s2)r1+2s1=r2+2s2r1+2s1(r2+2s2)=0(r1r2)+2(s1s2)=0(r1r2)+2(s1s2)=0+2

To determine

(b)

To check:

Whether J is onto or not.

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