Practice Symmetric Relations (17.2) - Irreflexive Relation - Discrete Mathematics

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6 sample questions

Question 1.
Define a symmetric relation in your own words.
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Think about bilateral relationships.
Question 2.
Is the relation {(1, 1), (1, 2)} symmetric?
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Check to see if the opposite pairs exist.
3Question 3.
What defines a symmetric relation?
- If (a
- b) implies (b
- a)
- If (a
- b) implies (a
- c)
- If (a
- a) is always present
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Consider the pairs and their relationships.
4Question 4.
True or False: A reflexive relation is always symmetric.
- True
- False
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Remember an example where reflexive does not mean symmetric.
Question 5.
Construct a symmetric relation for a set A = {1, 2, 3} and explain its properties.
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Ensure all necessary reciprocate pairs are included.
Question 6.
Prove whether a relation defined as R = {(1, 2), (2, 3), (1, 3)} can be symmetric.
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Check for reciprocal relationships.

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