   Chapter 7.2, Problem 23ES ### 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 F :   P ( { a ,   b ,   c } ) → Z as follaws: For every A in P ( { a ,   b ,   c } ) , F ( A ) = the number of elements in A.a. Is F one-to-one? Prove or give a counterexample. b. Is F onto? Prove or give a counterexample.

To determine

(a)

To check:

Whether F is one-to-one or not.

Explanation

Given information:

F:P({a,b,c}) is defined as follows:

For all A in P({a,b,c}), F(A)= the number of elements in A.

Concept used:

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

Calculation:

Clearly, {a,b},{b,c}P{a,b,c}

{a,b}{b<

To determine

(b)

To check:

Whether F is onto or not.

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