a.
Explain the given set is finite.
a.
Answer to Problem 3E
The set
Explanation of Solution
Given information:
Calculation:
Consider, definition and result for finite set,
Definition: the set
Result:
If a set
The given set is as,
So cardinality of set
Hence, set
b.
Explain the given set is finite.
b.
Answer to Problem 3E
Set
Explanation of Solution
Given information:
Calculation:
Consider, definition and result for finite set,
Definition: the set
Result:
If a set
The given set is as,
So the cardinality of set
Hence, set
c.
Explain the given set is finite.
c.
Answer to Problem 3E
Set
Explanation of Solution
Given information:
Calculation:
Consider, definition and result for finite set,
Definition: the set
Result:
If a set
The given set is as,
So the cardinality of set
Hence, set
d.
Explain the given set is finite.
d.
Answer to Problem 3E
Set
Explanation of Solution
Given information:
Calculation:
Consider, definition and result for finite set,
Definition: the set
Result:
If a set
The given set is as,
So the cardinality of set
Hence, set
e.
Explain the given set is finite.
e.
Answer to Problem 3E
Set
Explanation of Solution
Given information:
Calculation:
Consider, definition and result for finite set,
Definition: the set
Result:
If a set
The given set is as,
So the cardinality of set
Hence, set
f.
Explain the given set is finite.
f.
Answer to Problem 3E
Set
Explanation of Solution
Given information:
Calculation:
Consider, definition and result for finite set,
Definition: the set
Result:
If a set
The given set is as,
So the cardinality of set
Hence, set
g.
Explain the given set is finite.
g.
Answer to Problem 3E
Set
Explanation of Solution
Given information:
Calculation:
Consider, definition and result for finite set,
Definition: the set
Result:
If a set
The given set is as,
So the cardinality of the set
Hence, set
h.
Explain the given set is finite.
h.
Answer to Problem 3E
Set
Explanation of Solution
Given information:
Calculation:
Consider, definition and result for finite set,
Definition: the set
Result:
If a set
The given set is as,
So the cardinality of set
Hence, set
i.
Explain the given set is finite.
i.
Answer to Problem 3E
Set
Explanation of Solution
Given information:
Calculation:
Consider, definition and result for finite set,
Definition: the set
Result:
If a set
The given set is as,
So the cardinality of set
It implies that cardinality of set
Hence, set
j.
Explain the given set is finite.
j.
Answer to Problem 3E
Set
Explanation of Solution
Given information:
Calculation:
Consider, definition and result for finite set,
Definition: the set
Result:
If a set
The given set is as,
So
The maximum cardinality of set
Hence, the cardinality for given set
Hence, set
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Chapter 5 Solutions
A Transition to Advanced Mathematics
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- Let R be the set of all matrices of the form [abba], where a and b are real numbers. Assume that R is a commutative ring with unity with respect to matrix addition and multiplication. Answer the following questions and give a reason for any negative answers. Is 12 an integral domain? Is R a field?arrow_forwardLet R be a commutative ring with characteristic 2. Show that each of the following is true for all x,yR a. (x+y)2=x2+y2 b. (x+y)4=x4+y4arrow_forwardWrite out the addition and multiplication tables for 5.arrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning