Practice Definition of Groups - 13.1 | 13. Group Theory | Discrete Mathematics - Vol 3
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Definition of Groups

13.1 - Definition of Groups

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Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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.

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