Practice Group Axioms - 13.2 | 13. Group Theory | Discrete Mathematics - Vol 3
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Group Axioms

13.2 - Group Axioms

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the first axiom of a group?

💡 Hint: Consider what happens when you combine two numbers from the set.

Question 2 Easy

Is zero the identity element in the group of integers under addition?

💡 Hint: Think about adding zero to any number.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the closure property entail?

The operation can produce an element outside the set
The operation must produce an element within the set
It is an optional property

💡 Hint: Think about the results of combining elements from a set.

Question 2

True or False: An identity element must be unique within a group.

True
False

💡 Hint: Consider the implications of having multiple identity elements.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Consider the set of all integers. Prove whether it forms a group under subtraction.

💡 Hint: Think about operations and how subtraction behaves compared to addition.

Challenge 2 Hard

Given a set of matrices with a defined matrix addition, explain whether it can form a group and why.

💡 Hint: Do matrices behave like numbers in terms of addition?

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