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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Identify the identity element for the group of integers under addition.
💡 Hint: Think about what number you can add to any integer to get that integer back.
Question 2
Easy
Is the set of positive integers under addition a group? Why or why not?
💡 Hint: Consider if you have '0' or a similar number in that set.
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 is the identity element of the group of integers under addition?
- 1
- 2
- 0
💡 Hint: Look at what happens when you add 0.
Question 2
True or False: Every group is Abelian.
- True
- False
💡 Hint: Think about the order of operations in groups.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the identity element is unique in any group.
💡 Hint: Use the definitions of identity element properties in your proof.
Question 2
Consider a set of complex numbers under multiplication. Describe the identity element and prove its existence.
💡 Hint: Apply the definition of multiplication for complex numbers.
Challenge and get performance evaluation