Theory of Positive Integers : Function & Equivalence Relations

Study concepts, example questions & explanations for Theory of Positive Integers

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Example Questions

Example Question #1 : Function & Equivalence Relations

Which of the following is a property of a relation?

Possible Answers:

Symmetric Property

Partition Property

Equivalency Property

Non-symmetric Property

All are properties of a relation

Correct answer:

Symmetric Property

Explanation:

For a relation to exist there must be a non empty set present. If a non empty set is present then there are three relation properties.

These properties are:

I. Reflexive Property

II. Symmetric Property

III. Transitive Property

When all three properties represent a specific set, then that set is known to have an equivalence relation.

Example Question #2 : Function & Equivalence Relations

What is an equivalency class?

Possible Answers:

Correct answer:

Explanation:

An equivalency class is a definitional term.

Suppose  is a non empty set and  is an equivalency relation on . Then  belonging to  is a set that holds all the elements that live in  that are equivalent to .

In mathematical terms this looks as follows,

Example Question #3 : Function & Equivalence Relations

Which of the following is a property of a relation?

Possible Answers:

Reflexive Property

All are relation properties

Equivalency Property

Associative Property

Non-symmetric Property

Correct answer:

Reflexive Property

Explanation:

For a relation to exist there must be a non empty set present. If a non empty set is present then there are three relation properties.

These properties are:

I. Reflexive Property

II. Symmetric Property

III. Transitive Property

When all three properties represent a specific set, then that set is known to have an equivalence relation.

Example Question #4 : Function & Equivalence Relations

Which of the following is a property of a relation?

Possible Answers:

Partition Property

Equivalency Property

All are properties of relations.

Non-symmetric Property

Transitive Property

Correct answer:

Transitive Property

Explanation:

For a relation to exist there must be a non empty set present. If a non empty set is present then there are three relation properties.

These properties are:

I. Reflexive Property

II. Symmetric Property

III. Transitive Property

When all three properties represent a specific set, then that set is known to have an equivalence relation.

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