13.6.2 - Group Order
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Practice Questions
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Define the closure property in your own words.
💡 Hint: Think about adding two integers.
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.
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Interactive Quizzes
Quick quizzes to reinforce your learning
Which of the following is NOT a group axiom?
💡 Hint: Remember that not all operations have to be commutative.
True or False: The identity element of a group must be unique.
💡 Hint: Consider how identity relates to every other element.
1 more question available
Challenge Problems
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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.
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.
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