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Practice Questions
Test your understanding with targeted questions related to the topic.
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?
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
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.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation