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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

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Section
BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
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a. Show that the mapping f given in Example 2 is neither onto nor one-to-one.

b. For this mapping f , show that if S = { 1 , 2 } , then f 1 ( f ( S ) ) S .

c. For this same f and T = { 4 , 9 } , show that f ( f 1 ( T ) ) T .

a)

To determine

To prove: Mapping f is neither onto nor one-to-one.

Explanation

Given Information:

Let A={2,1,2} and let B={1,4,9}. The set f given by,

f(x)={(2,4),(1,1),(2,4)}

Explanation:

Let f:XY

Function f is called one-to-one, if and only if different elements of A always have different images under f.

Function f is called onto if and only if f(x)=y.

Let A={2,1,2} and let B={1,4,9}

b)

To determine

To prove: If S={1,2} then f1(f(S))S.

c)

To determine

To prove: The statement “f(f1(T))T”.

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