Practice Examples of Groups - 13.3 | 13. Group Theory | Discrete Mathematics - Vol 3
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Examples of Groups

13.3 - Examples of Groups

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What does closure mean in group theory?

💡 Hint: Think about what happens when you add two integers.

Question 2 Easy

Identify the identity element in the group of integers with addition.

💡 Hint: What number serves as a neutral element in addition?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

Which of the following is not a property of a group?

Closure
Distributivity
Identities

💡 Hint: Focus on the fundamental group axioms.

Question 2

True or False: The set of natural numbers (excluding zero) is a group under addition.

True
False

💡 Hint: Consider addition's identity and inverses.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Demonstrate that the set of matrices of size 2x2 under addition forms a group.

💡 Hint: Consider how matrices add together and whether their operations fit the group properties.

Challenge 2 Hard

Prove that the group of integers modulo n under addition isn't an abelian group if n is odd.

💡 Hint: Consider how addition behaves under modulo conditions with odd-equal sums.

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