Practice Reflexive Closure (18.7.1) - Operations on Relations - Discrete Mathematics - Vol 1

Practice: Reflexive Closure

Lesson 18.7.1Operations on Relations

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9 questions

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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 how elements relate to themselves.
Question 2.
Given a set A = {1, 2, 3} and a relation R = {(1, 2)}, what pairs need to be added for it to be reflexive?
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Self-referencing pairs are necessary.
3Question 3.
What is the reflexive closure of a relation?
- A new relation excluding existing pairs
- The smallest superset containing (a
- a) pairs
- A relation with no pairs
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Think about examples of relations that include self-references.
4Question 4.
True or False: The reflexive closure can lead to the addition of duplicate pairs.
- True
- False
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Remember the properties of union in set theory.
Question 5.
Create a reflexive closure for the relation R = {(1, 2), (2, 3)} over the set A = {1, 2, 3}. What is the resulting relation?
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Make sure to include all necessary self-references.
Question 6.
In a network of friends, if R denotes relationships, how would you explain the reflexive closure in terms of social ties?
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Consider self-identification in a social context.

5 more questions in this section. Enroll free to practise them all.