Practice Closure Property (13.2.1) - Group Theory - Discrete Mathematics

Practise this section

8 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What does the closure property state?
Show hintHide hint
Think about operations like addition or multiplication.
Question 2.
Give an example of a set that satisfies closure under addition.
Show hintHide hint
Consider what happens when you add two integers together.
3Question 3.
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.
Show hintHide hint
Think about the definition of closure.
4Question 4.
True or False: The set of integers under subtraction is a group.
- True
- False
Show hintHide hint
Think about what happens when you subtract.
Question 5.
Prove that the set of all even integers under addition forms a group and determine its closure.
Show hintHide hint
Start with defining even integers mathematically.
Question 6.
Consider three operations: +, ×, and modulo. Can a set be closed under one operation but not the others? Provide an example.
Show hintHide hint
Examine closure concerning modular arithmetic.

4 more questions in this section. Enroll free to practise them all.