Practice Examples Of Equivalence Classes (21.5)

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6 sample questions

Question 1.
What does it mean for a relation to be reflexive?
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Think about a number interacting with itself.
Question 2.
Give an example of an equivalence class in mod 3.
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Consider what results when you divide the integers by 3.
3Question 3.
What property states that if a is related to b, then b is also related to a?
- Reflexivity
- Symmetry
- Transitivity
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Think about how relationships mirror each other.
4Question 4.
True or False: An equivalence class can be empty.
- True
- False
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Recall the property of every equivalence class.
Question 5.
Given the relation a ≡ b (mod 4), determine whether pairs (6, 10) and (2, 6) belong to the same equivalence class. Justify your answer.
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Check the remainder of each number when divided by 4.
Question 6.
Prove that all integers can be classified under an equivalence relation based on their remainders when divided by n for any integer n > 0.
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Utilize a proof by contradiction regarding shared remainders.

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