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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define the closure property in your own words.
💡 Hint: Think about adding two integers.
Question 2
Easy
What is the identity element in the group of integers under addition?
💡 Hint: Consider what number you can add to any integer without changing its value.
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 of the following is NOT a group axiom?
- Closure
- Associativity
- Commutativity
- Inverse
💡 Hint: Remember that not all operations have to be commutative.
Question 2
True or False: The identity element of a group must be unique.
- True
- False
💡 Hint: Consider how identity relates to every other element.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the set of rational numbers excluding zero under multiplication, prove or disprove that it forms a group.
💡 Hint: Establish closure by multiplying two rationals and see if the result is rational.
Question 2
Construct a finite group using a set of elements {0, 1, 2} under addition modulo 3, and verify all group properties.
💡 Hint: Perform addition and standard mod operations for verification.
Challenge and get performance evaluation