Practice Question 3 (21.4) - Lecture -20 - Discrete Mathematics

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6 sample questions

Question 1.
What is a symmetric relation?
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Consider how pairs are related.
Question 2.
Provide an example of an anti-symmetric relation.
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Think about how elements relate when they are equal.
3Question 3.
Which of the following pairs must both be present for a symmetric relation?
- (i
- j)
- (i
- j)
- (j
- i)
- (i
- k)
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Think about how the pairs relate to each other.
4Question 4.
True or False: All reflexive relations are also symmetric.
- True
- False
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Consider the definitions of both properties.
Question 5.
Given a set of 5 elements, calculate the number of different symmetric relations possible. Show your workings.
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Focus on how each pair can be chosen.
Question 6.
Explain why a relation that is both reflexive and asymmetric cannot exist. Provide a contradiction.
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Consider the definitions and how they interact.

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