Equivalence Relations Quiz

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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?

Equality of numbers (correct)

Inequality of numbers

Addition of numbers

Subtraction of numbers

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?

a ∼ b Signup and view all the answers

What is the equipollence relation between line segments in geometry an example of?

An equivalence relation Signup and view all the answers

What is the domain of a function?

The set of all possible input values for the function Signup and view all the answers

How is a function most often denoted?

By letters such as f, g, and h Signup and view all the answers

What does the notation f(x) represent?

The value of function f at the element x of its domain Signup and view all the answers

When was the concept of a function formalized in terms of set theory?

End of the 19th century Signup and view all the answers

What was historically the idealization of how a varying quantity depends on another quantity?

Functions Signup and view all the answers

Equivalence Relations Quiz

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Questions and Answers

What are the three properties that an equivalence relation must satisfy?

Which of the following is an example of an equivalence relation?

What does an equivalence relation provide for the underlying set?

Which notation is commonly used to denote equivalence of elements a and b with respect to an equivalence relation R?

What is the equipollence relation between line segments in geometry an example of?

What is the domain of a function?

How is a function most often denoted?

What does the notation f(x) represent?

When was the concept of a function formalized in terms of set theory?

What was historically the idealization of how a varying quantity depends on another quantity?

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