Practice Definition Of A Relation (1.1) - Relations and Functions

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6 sample questions

Question 1.
Define a relation in your own words.
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Think about how elements from two sets can be paired.
Question 2.
What is a reflexive relation? Give an example.
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Consider a relation that includes pairs of the same elements.
3Question 3.
What defines a relation in mathematics?
- A set of single elements
- A subset of the Cartesian product of two sets
- A collection of functions
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Think about how we can pair elements from two sets.
4Question 4.
True or False: A symmetric relation must also be reflexive.
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Consider whether all elements must relate to themselves.
Question 5.
Create a set A and a relation R that is reflexive, symmetric, and transitive but has no additional pairs (like anti-symmetry). Explain your reasoning.
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Consider how adding pairs affects the properties you are establishing.
Question 6.
Given a relation R = {(1, 2), (2, 3), (3, 4)}, is it transitive? Justify your answer.
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Check pairs for forward chaining to verify transitivity.

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