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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What property ensures that the operation between any two elements of a group results in an element within the set?
💡 Hint: Think about the 'closure' of a set.
Question 2
Easy
What is the identity element when using multiplication in a group of non-zero real numbers?
💡 Hint: What number keeps other numbers the same when multiplied?
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 property guarantees that the product of two elements is still within the set?
- Closure
- Identity
- Inverse
💡 Hint: Think about what happens when you add two elements.
Question 2
True or False: Every integer has a multiplicative inverse within the set of integers.
- True
- False
💡 Hint: Consider if dividing integers always yields integers.
Solve 3 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Create a set that fails to meet the group axioms and identify which axiom is violated.
💡 Hint: Explore what happens with the operation on elements of this set.
Question 2
Prove that addition of integers is a group.
💡 Hint: Use the definitions of axioms to support your argument.
Challenge and get performance evaluation