Practice Abstract Groups (13.6) - Group Theory - Discrete Mathematics

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9 questions

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6 sample questions

Question 1.
What is the identity element in the group of integers under addition?
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Think about what number added to any integer gives the same integer.
Question 2.
True or False: The set of all even integers forms a group under addition.
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Check if all group properties are satisfied.
3Question 3.
What are the properties that must be satisfied for a set to be a group?
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List down each property.
4Question 4.
True or False: A set must always have a commutative operation to be considered a group.
- True
- False
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Recall the definition of Abelian groups.
Question 5.
Prove that the set of rational numbers excluding zero forms a group under multiplication.
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Verify closure first.
Question 6.
Create an abstract group operation that meets all the properties but is not traditional addition or multiplication.
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Think outside numeric operations.

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