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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the definition of a group?
💡 Hint: Remember the four key properties.
Question 2
Easy
Can a set of non-negative integers form a group under addition?
💡 Hint: Consider what happens when you try to find the inverse of an element.
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 defines a group in mathematics?
- A set with addition
- A set with a binary operation satisfying certain axioms
- Any collection of numbers
💡 Hint: Think about the requirements needed for a group.
Question 2
Is the identity element unique in a group?
- True
- False
💡 Hint: Consider the definition of identity in groups.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider the set of rational numbers under addition. Does it form a group? Justify your answer using the group axioms.
💡 Hint: Check each axiom systematically.
Question 2
Propose a new operation on a set of your choice and prove whether or not it forms a group.
💡 Hint: Define your operation clearly and work through examples.
Challenge and get performance evaluation