Function & Equivalence Relations - Theory of Positive Integers

Card 0 of 16

Question

Which of the following is a property of a relation?

Answer

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

$x\approx x$

II. Symmetric Property

$x\approx y\rightarrow y\approx x$

III. Transitive Property

$x\approx y, y\approx z \rightarrow x\approx z$

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

Compare your answer with the correct one above

Question

What is an equivalency class?

Answer

An equivalency class is a definitional term.

Suppose is a non empty set and $\approx$ 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,

$[x]=\begin{Bmatrix} y\ \epsilon\ A, x\approx y \end{Bmatrix}$

Compare your answer with the correct one above

Question

Which of the following is a property of a relation?

Answer

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

$x\approx x$

II. Symmetric Property

$x\approx y\rightarrow y\approx x$

III. Transitive Property

$x\approx y, y\approx z \rightarrow x\approx z$

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

Compare your answer with the correct one above

Question

Which of the following is a property of a relation?

Answer

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

$x\approx x$

II. Symmetric Property

$x\approx y\rightarrow y\approx x$

III. Transitive Property

$x\approx y, y\approx z \rightarrow x\approx z$

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

Compare your answer with the correct one above

Question

Which of the following is a property of a relation?

Answer

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

$x\approx x$

II. Symmetric Property

$x\approx y\rightarrow y\approx x$

III. Transitive Property

$x\approx y, y\approx z \rightarrow x\approx z$

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

Compare your answer with the correct one above

Question

What is an equivalency class?

Answer

An equivalency class is a definitional term.

Suppose is a non empty set and $\approx$ 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,

$[x]=\begin{Bmatrix} y\ \epsilon\ A, x\approx y \end{Bmatrix}$

Compare your answer with the correct one above

Question

Which of the following is a property of a relation?

Answer

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

$x\approx x$

II. Symmetric Property

$x\approx y\rightarrow y\approx x$

III. Transitive Property

$x\approx y, y\approx z \rightarrow x\approx z$

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

Compare your answer with the correct one above

Question

Which of the following is a property of a relation?

Answer

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

$x\approx x$

II. Symmetric Property

$x\approx y\rightarrow y\approx x$

III. Transitive Property

$x\approx y, y\approx z \rightarrow x\approx z$

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

Compare your answer with the correct one above

Question

Which of the following is a property of a relation?

Answer

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

$x\approx x$

II. Symmetric Property

$x\approx y\rightarrow y\approx x$

III. Transitive Property

$x\approx y, y\approx z \rightarrow x\approx z$

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

Compare your answer with the correct one above

Question

What is an equivalency class?

Answer

An equivalency class is a definitional term.

Suppose is a non empty set and $\approx$ 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,

$[x]=\begin{Bmatrix} y\ \epsilon\ A, x\approx y \end{Bmatrix}$

Compare your answer with the correct one above

Question

Which of the following is a property of a relation?

Answer

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

$x\approx x$

II. Symmetric Property

$x\approx y\rightarrow y\approx x$

III. Transitive Property

$x\approx y, y\approx z \rightarrow x\approx z$

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

Compare your answer with the correct one above

Question

Which of the following is a property of a relation?

Answer

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

$x\approx x$

II. Symmetric Property

$x\approx y\rightarrow y\approx x$

III. Transitive Property

$x\approx y, y\approx z \rightarrow x\approx z$

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

Compare your answer with the correct one above

Question

Which of the following is a property of a relation?

Answer

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

$x\approx x$

II. Symmetric Property

$x\approx y\rightarrow y\approx x$

III. Transitive Property

$x\approx y, y\approx z \rightarrow x\approx z$

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

Compare your answer with the correct one above

Question

What is an equivalency class?

Answer

An equivalency class is a definitional term.

Suppose is a non empty set and $\approx$ 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,

$[x]=\begin{Bmatrix} y\ \epsilon\ A, x\approx y \end{Bmatrix}$

Compare your answer with the correct one above

Question

Which of the following is a property of a relation?

Answer

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

$x\approx x$

II. Symmetric Property

$x\approx y\rightarrow y\approx x$

III. Transitive Property

$x\approx y, y\approx z \rightarrow x\approx z$

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

Compare your answer with the correct one above

Question

Which of the following is a property of a relation?

Answer

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

$x\approx x$

II. Symmetric Property

$x\approx y\rightarrow y\approx x$

III. Transitive Property

$x\approx y, y\approx z \rightarrow x\approx z$

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

Compare your answer with the correct one above

Tap the card to reveal the answer

Function & Equivalence Relations - Theory of Positive Integers

Which of the following is a property of a relation?

What is an equivalency class?

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,

Which of the following is a property of a relation?

Which of the following is a property of a relation?

Which of the following is a property of a relation?

What is an equivalency class?

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,

Which of the following is a property of a relation?

Which of the following is a property of a relation?

Which of the following is a property of a relation?

What is an equivalency class?

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,

Which of the following is a property of a relation?

Which of the following is a property of a relation?

Which of the following is a property of a relation?

What is an equivalency class?

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,

Which of the following is a property of a relation?

Which of the following is a property of a relation?