13.2.1 - Closure Property
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Practice Questions
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What does the closure property state?
💡 Hint: Think about operations like addition or multiplication.
Give an example of a set that satisfies closure under addition.
💡 Hint: Consider what happens when you add two integers together.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is required for a set to satisfy the closure property?
💡 Hint: Think about the definition of closure.
True or False: The set of integers under subtraction is a group.
💡 Hint: Think about what happens when you subtract.
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Challenge Problems
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Prove that the set of all even integers under addition forms a group and determine its closure.
💡 Hint: Start with defining even integers mathematically.
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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