3. C=Z+, (a*b) = ([max(a,b)]/8) + 3 %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Answer no. 3 and 4 only. Make sure to do it completely and follow the instructions. Don't forget to fill out the table too. Typewritten for upvote. Thank you
![Instructions:
For every item given below, determine which kind of algebraic structure it is, and give at least one proof of
why it is not of the higher structure (e.g. it is a semigroup but not a monoid because it doesn't have an
identity element, etc.). Make a table like the one below. Put a check(/) if it satisfies the property, cross (X),
otherwise.
If it is a semigroup, show associativity by giving proof or examples.
If it is a commutative semigroup, show commutativity by giving proof or examples.
If it is a monoid, identify the identity element through computation.
If it is a group, identify the inverse element through computation.
If it is an abelian group, show commutativity by giving proof or examples.
Explain how you arrived at your answers. Please note this notations: Z = set of integers, Q = set of rational
numbers, R=set of real numbers, Z+ and Q+ = positive numbers, e = positive numbers including zero
1. A = R, (a*b) = a+b
2. B=Z, (a*b) = a+b
3. C=Z+, (a*b) = ([max(a,b)]/8) + 3
4. D= Q+, (a*b) = (a · b)/4
5. E=Z+, (a*b) = (a · b)/5
6. F= Q, (a*b) = (Imax(a,b)]/b) - 9
7. G=Z+, (a*b) = |min(a,b)\/a
8. H= Q+, (a*b) = (a+b) + 10
9. 1= set of all positive even integers, (a*b) = (a-b)/2
10. J = set of all positive odd integers, (a*b) = 2(a-b) + 1
*where · is a dot product or multiplication
*where is a dot product or multiplication
"where - is subtraction
"where |. is absolute value
No.
Groupoid
Semigroup
Commutative Semigroup
Monoid
Group
Abelian Group
1
3
4
5
6
7
8
9
10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a92f4fb-ddb9-4f5e-a342-db4e205f2dae%2Fae180193-cf29-4326-8cae-b64db9fb7369%2F250k54s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Instructions:
For every item given below, determine which kind of algebraic structure it is, and give at least one proof of
why it is not of the higher structure (e.g. it is a semigroup but not a monoid because it doesn't have an
identity element, etc.). Make a table like the one below. Put a check(/) if it satisfies the property, cross (X),
otherwise.
If it is a semigroup, show associativity by giving proof or examples.
If it is a commutative semigroup, show commutativity by giving proof or examples.
If it is a monoid, identify the identity element through computation.
If it is a group, identify the inverse element through computation.
If it is an abelian group, show commutativity by giving proof or examples.
Explain how you arrived at your answers. Please note this notations: Z = set of integers, Q = set of rational
numbers, R=set of real numbers, Z+ and Q+ = positive numbers, e = positive numbers including zero
1. A = R, (a*b) = a+b
2. B=Z, (a*b) = a+b
3. C=Z+, (a*b) = ([max(a,b)]/8) + 3
4. D= Q+, (a*b) = (a · b)/4
5. E=Z+, (a*b) = (a · b)/5
6. F= Q, (a*b) = (Imax(a,b)]/b) - 9
7. G=Z+, (a*b) = |min(a,b)\/a
8. H= Q+, (a*b) = (a+b) + 10
9. 1= set of all positive even integers, (a*b) = (a-b)/2
10. J = set of all positive odd integers, (a*b) = 2(a-b) + 1
*where · is a dot product or multiplication
*where is a dot product or multiplication
"where - is subtraction
"where |. is absolute value
No.
Groupoid
Semigroup
Commutative Semigroup
Monoid
Group
Abelian Group
1
3
4
5
6
7
8
9
10
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