Practice Group Of Integers Under Addition (13.3.1) - Group Theory - Discrete Mathematics - Vol 3

Practice: Group of Integers under Addition

Lesson 13.3.1Group Theory

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10 questions

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6 sample questions

Question 1.
What is the identity element for the group of integers under addition?
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Think about what number does not change another number when added.
Question 2.
State one property of a group.
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There are multiple properties to choose from.
3Question 3.
What does the closure property imply in the context of groups?
- The operation must be commutative.
- The result of the operation on any two elements must be within the set.
- There must be an identity element in the set.
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Reflect on the examples of groups we've covered.
4Question 4.
True or False: Every element in a group has an inverse.
- True
- False
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Think about the properties that define a group.
Question 5.
If a group has elements {1, 2, 3} under addition mod 4, list all possible sums of two elements and analyze if this set forms a group.
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Consider closure and whether each result remains in the set.
Question 6.
Given the integers with an operation augmented by a new 'twist' where n=3 (addition mod 3), what are the group properties? List inverses.
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Examine how mod 3 affects numbers and which results stay within our defined set.

6 more questions in this section. Enroll free to practise them all.