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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the identity element in the group of integers under addition?
💡 Hint: Think about what number added to any integer gives the same integer.
Question 2
Easy
True or False: The set of all even integers forms a group under addition.
💡 Hint: Check if all group properties are satisfied.
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
What are the properties that must be satisfied for a set to be a group?
💡 Hint: List down each property.
Question 2
True or False: A set must always have a commutative operation to be considered a group.
- True
- False
💡 Hint: Recall the definition of Abelian groups.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the set of rational numbers excluding zero forms a group under multiplication.
💡 Hint: Verify closure first.
Question 2
Create an abstract group operation that meets all the properties but is not traditional addition or multiplication.
💡 Hint: Think outside numeric operations.
Challenge and get performance evaluation