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Questions and Answers
What are the three properties that an equivalence relation must satisfy?
What are the three properties that an equivalence relation must satisfy?
- Reflexive, antisymmetric, and transitive
- Reflexive, symmetric, and transitive (correct)
- Symmetric, transitive, and antisymmetric
- Reflexive, symmetric, and antisymmetric
Which of the following is an example of an equivalence relation?
Which of the following is an example of an equivalence relation?
- Equality of numbers (correct)
- Inequality of numbers
- Addition of numbers
- Subtraction of numbers
What does an equivalence relation provide for the underlying set?
What does an equivalence relation provide for the underlying set?
- No partitioning
- A partition into overlapping equivalence classes
- A partition into disjoint equivalence classes (correct)
- A single equivalence class
Which notation is commonly used to denote equivalence of elements a and b with respect to an equivalence relation R?
Which notation is commonly used to denote equivalence of elements a and b with respect to an equivalence relation R?
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What is the equipollence relation between line segments in geometry an example of?
What is the equipollence relation between line segments in geometry an example of?
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What is the domain of a function?
What is the domain of a function?
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How is a function most often denoted?
How is a function most often denoted?
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What does the notation f(x) represent?
What does the notation f(x) represent?
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When was the concept of a function formalized in terms of set theory?
When was the concept of a function formalized in terms of set theory?
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What was historically the idealization of how a varying quantity depends on another quantity?
What was historically the idealization of how a varying quantity depends on another quantity?
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