Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What are the four axioms that define a group?
💡 Hint: Use the acronym C-A-I-I.
Question 2
Easy
Give an example of a group under addition.
💡 Hint: Think about the properties of integers.
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 ensures that the result of an operation on two elements is still in the set?
- Closure
- Associativity
- Identity
💡 Hint: Think about how operations interact with set membership.
Question 2
True or False: Every group operation must be commutative.
- True
- False
💡 Hint: Recall the definition of an Abelian group.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that any finite subset of a group is also a group under the same binary operation, citing each of the group axioms.
💡 Hint: Focus on the properties of the larger group.
Question 2
Given the set of integers modulo n, discuss how it forms a group with addition, relating it to all four axioms.
💡 Hint: Revisit properties of modulo arithmetic.
Challenge and get performance evaluation