Mathematics Relations Overview

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What does the term 'relation' refer to in mathematics?

A method for solving equations
A direct comparison between numbers
A procedure that associates some elements of one set to another (correct)
A constant value

The sets A and B can be empty for a relation to be defined.

False (B)

Give an example of a property that could establish a relation between two sets.

The word x contains the letter y.

In the relation defined in the content, 'star' is in relation with _____ because it contains the letter 'a'.

a Signup and view all the answers

Match the following terms with their definitions:

Set A = The starting set Set B = The arrival set Relation = A procedure that associates elements from two sets Property = An open statement used to define relations Signup and view all the answers

What represents the elements of a set in a graph?

Nodes (D) Signup and view all the answers

A graph can represent only one relation at a time.

False (B) Signup and view all the answers

What type of connection is used to depict that element x is in relation with itself in a graph?

A loop around node x Signup and view all the answers

To show that nodes x and y are not in relation, you should ___ connect them with an arrow.

not Signup and view all the answers

Match the following descriptions with their corresponding graph representations:

x is in relation with y = A directed arrow from x to y x is in relation with itself = A loop around node x x is in relation with y and y is in relation with x = A two-headed arrow between nodes x and y x and y are not in relation = No arrow connecting nodes x and y Signup and view all the answers

In the relation notation xRy, what does y represent?

The image of x (B) Signup and view all the answers

The elements of set A that have at least one image in set B are considered part of the image.

False (B) Signup and view all the answers

What is the relationship between elements in sets A and B represented in a diagram?

Arrows Signup and view all the answers

The ________ consists of all elements in set A from which at least one arrow originates.

domain Signup and view all the answers

Match the following representations of a relationship with their descriptions:

Elencazione = Listing elements Diagramma a frecce = Use arrows to depict relations Tabella a doppia entrata = A table to visually represent relations Diagramma cartesiano = A Cartesian plane graph Signup and view all the answers

Which representation method uses arrows to show relations between elements in sets A and B?

Arrow diagram (A) Signup and view all the answers

A relation is always defined by an explicit property that links elements from set A to set B.

False (B) Signup and view all the answers

What is the graph of relation R for sets A = {2, 3, 4} and B = {4, 5, 6}?

{(2, 5), (3, 4), (3, 5), (4, 5)} Signup and view all the answers

In a table with double entry, a symbol is placed in the cell to indicate that the corresponding pairs are in relation, typically represented by a _______.

checkmark Signup and view all the answers

Match the following representation methods with their descriptions:

Arrow diagram = Visually connects elements to show relationships Table with double entry = Marks cells to indicate relations Cartesian diagram = Plots points corresponding to pairs in R Representation by listing = Lists ordered pairs of related elements Signup and view all the answers

Domain of a relation

The set of all elements in A that have at least one image in B.

Image of a relation

The set of all elements in B that are images of elements in A.

Image of an element

An element y in B is called the image of an element x in A if there is a relation R connecting x to y. This means xRy.

Inverse image of an element

An element x in A is called the inverse image of an element y in B if there is a relation R connecting y to x. This means yRx.