Practice Part (a): Symmetric And Transitive Relations (2.6.1)

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6 sample questions

Question 1.
Define a symmetric relation with an example.
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Think about how friendships work!
Question 2.
What does it mean for a relation to be transitive?
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Consider a chain of relationships!
3Question 3.
What is a symmetric relation?
- If aRb then bRa
- If aRb then aRc
- No specific property
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Recall definitions of relations.
4Question 4.
True or False: All transitive relations are also symmetric.
- True
- False
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Consider the definitions carefully.
Question 5.
Prove whether the relation defined by R = {(1, 2), (2, 3), (3, 1)} is transitive.
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Check the connections between the elements carefully.
Question 6.
Construct a relation R on a set A = {a, b, c, d} that is symmetric and give a counterexample to show why R can be transitive but not reflexive.
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Always ensure to list all pairs thoroughly.

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