### All Theory of Positive Integers Resources

## Example Questions

### Example Question #1 : Function & Equivalence Relations

Which of the following is a property of a relation?

**Possible Answers:**

Equivalency Property

All are properties of a relation

Partition Property

Non-symmetric Property

Symmetric Property

**Correct answer:**

Symmetric Property

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:**

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:**

Equivalency Property

Non-symmetric Property

All are relation properties

Associative Property

Reflexive Property

**Correct answer:**

Reflexive Property

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:**

All are properties of relations.

Non-symmetric Property

Equivalency Property

Transitive Property

Partition Property

**Correct answer:**

Transitive Property

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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### All Theory of Positive Integers Resources

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