Practice Question 4 (21.5) - Lecture -20 - Discrete Mathematics

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6 sample questions

Question 1.
What does it mean for a relation to be symmetric?
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Think about mutual connections.
Question 2.
Give an example of a reflexive relation.
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Self-relationships are key.
3Question 3.
Which type of relation includes both (a, b) and (b, a) pairs?
- Reflexive
- Symmetric
- Irreflexive
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Think about bidirectional relationships.
4Question 4.
True or False: An irreflexive relation contains at least one pair (a, a).
- True
- False
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Consider the definition of irreflexivity.
Question 5.
Create a relation on set S = {1, 2, 3} that is reflexive but neither symmetric nor anti-symmetric.
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Think of adding relationships that contradict those properties.
Question 6.
Given a relation that is symmetric, can you prove it is also reflexive if it includes pairs like (a, a) for some a?
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Visualize the elements involved.

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