Practice Equivalence Relation (1.2.5) - Relations and Functions

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6 sample questions

Question 1.
What is the definition of an equivalence relation?
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Think about the properties that must be satisfied.
Question 2.
Give an example of a reflexive relation.
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Consider pairs where the elements are the same.
3Question 3.
Which of the following properties must an equivalence relation satisfy?
- Reflexive
- Symmetric
- Transitive
- All of the above
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Recall the definition of equivalence relation.
4Question 4.
True or False: The relation R = {(1,2),(2,3)} is an equivalence relation.
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Consider what reflexivity entails.
Question 5.
Prove that the relation R = {(1,1), (1,2), (2,1), (2,2), (2,3), (3,2)} on set A = {1, 2, 3} is an equivalence relation.
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Verify each property meticulously.
Question 6.
Consider the relation R defined on set B = {a, b, c} with R = {(a,a), (b,b), (c,c), (a,b), (b,a)}. Is R equilibrium? Justify.
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Step through each property.

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