1.2.5 - Equivalence Relation
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Practice Questions
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What is the definition of an equivalence relation?
💡 Hint: Think about the properties that must be satisfied.
Give an example of a reflexive relation.
💡 Hint: Consider pairs where the elements are the same.
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Interactive Quizzes
Quick quizzes to reinforce your learning
Which of the following properties must an equivalence relation satisfy?
💡 Hint: Recall the definition of equivalence relation.
True or False: The relation R = {(1,2),(2,3)} is an equivalence relation.
💡 Hint: Consider what reflexivity entails.
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Challenge Problems
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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.
💡 Hint: Verify each property meticulously.
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.
💡 Hint: Step through each property.
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