Practice Closure Property - 13.2.1 | 13. Group Theory | Discrete Mathematics - Vol 3
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Closure Property

13.2.1 - Closure Property

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What does the closure property state?

💡 Hint: Think about operations like addition or multiplication.

Question 2 Easy

Give an example of a set that satisfies closure under addition.

💡 Hint: Consider what happens when you add two integers together.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is required for a set to satisfy the closure property?

The result must be outside the set.
The result must be an element of the set.
The set must be finite.

💡 Hint: Think about the definition of closure.

Question 2

True or False: The set of integers under subtraction is a group.

True
False

💡 Hint: Think about what happens when you subtract.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove that the set of all even integers under addition forms a group and determine its closure.

💡 Hint: Start with defining even integers mathematically.

Challenge 2 Hard

Consider three operations: +, ×, and modulo. Can a set be closed under one operation but not the others? Provide an example.

💡 Hint: Examine closure concerning modular arithmetic.

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