Practice Examples Of Transitive Relations (17.5.2)

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6 sample questions

Question 1.
Is the relation R = {(1, 1), (2, 3)} irreflexive?
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Recall that an irreflexive relation cannot contain (a, a).
Question 2.
Is R = {(1, 2), (2, 1)} symmetric?
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Check if both directional relations are included.
3Question 3.
What is an irreflexive relation?
- A relation where some elements relate to themselves
- A relation where no elements relate to themselves
- A relation with all elements relating to each other
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Recall the definition of irreflexive.
4Question 4.
True or False: Every symmetric relation is also antisymmetric.
- True
- False
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Think about how symmetry contradicts antisymmetry.
Question 5.
Given a relation R = {(1, 2), (2, 1), (2, 3)}, determine if R is symmetric, antisymmetric, or both.
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Examine the conditions set by the definitions.
Question 6.
If a relation defined on a set A is both symmetric and antisymmetric, under what conditions does this occur?
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Think about how each definition constrains relationships.

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