Practice Part C: Symmetric And Anti-symmetric Relations (21.5.3)

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6 sample questions

Question 1.
Define a symmetric relation and provide one example.
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Think about relationships where both parties have mutual recognition.
Question 2.
What characterizes an anti-symmetric relation?
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Consider scenarios where equality plays a role.
3Question 3.
True or False: A symmetric relation must have both (a,b) and (b,a) present if one exists.
- True
- False
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Check how the elements must relate to each other.
4Question 4.
Which of the following represents an example of an anti-symmetric relation? A: (1,2) and (2,1) B: (2,3) only C: (4,4) both as (a,a) is acceptable
- A
- B
- C
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Determine if either (a,b) or (b,a) can coexist.
Question 5.
Given a set of size 5, calculate the total number of symmetric relations. Show the step-by-step process.
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Recall the formula involves n choose pairs.
Question 6.
Construct a set of elements and create both a symmetric and an anti-symmetric relation. Explain the choices.
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Think about the directionality involved.

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