Practice Theorem On Equivalence Classes (21.8) - Equivalence Relation - Discrete Mathematics

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6 sample questions

Question 1.
What are the three properties of an equivalence relation?
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Think of the acronym RST.
Question 2.
Is (2, 2) in a relation R considered reflexive?
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Check if it holds true for any a.
3Question 3.
What property requires that an element be related to itself in an equivalence relation?
- Symmetric
- Transitive
- Reflexive
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Think of 'self-relationship'.
4Question 4.
True or False: In an equivalence relation, if a is related to b, then b must be related to a.
- True
- False
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Remember the 'back and forth' characteristic.
Question 5.
Given a set of integers and a relation defined as a ≡ b (mod 5), classify the integers based on their equivalence classes.
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Consider the remainders when each integer is divided by 5.
Question 6.
Prove that if two equivalence classes have any element in common, they are the same class.
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Think about how elements are classified in equivalence relations.

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