Relation of sets

Relation

While you may be seeking a better hand on functions and relations, it may be important to get to explore different elements included within the same.

What is a Relation?

Relation is said to determine the relationship that prevails between different sets of values. In Mathematics, this relation exists among the values x and y that are known to form the ordered sets. The set that carries x values is called the domain and the set that carries the y values is addressed as the range.

domain-range.png

In the above image, it could be seen that domain includes the x values from each of the ordered pairs and range consist of the y values from them. The brackets indicate that these values are forming a set. It is quite important to not repeat values in range sets and domain sets. These values can differ largely based on what is the actual need and prevailing situation.

Displaying Relations

Relations could be displayed either as a table, graph or a mapping.

Table

table.jpg

In the above table, the x and y values have been separately listed in different columns. Also, each row is said to represent and ordered pair.

Mapping

mapping.jpg

In mapping the domain and range are displayed as different clusters of values. The lines have been drawn in order to match all values in the domain to their corresponding values in the range set.

Graph

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Graphs could be used to show the relationships between various values. Every ordered pair is supposed to be plotted on the graph in the form of dots. The corresponding placement of the points along the x and the y axes determines the x and y values for the respective ordered pairs.

Some Examples

Consider an example where you’ve been asked to create a list of ordered pairs from the set of domain and range values as listed like (1,6), (5,0) etc. however, it could not be assumed that the values in the sets are all ordered and match the values in the sets. Also, it may be important to consider the fact that there could be different number of elements in each set i.e. domain and range. Therefore, it becomes important to focus on the right display of elements for the x values and the y values so that they can be paired up easily into ordered sets. Creating a list of ordered pairs becomes sophisticated with the help of various methods of displaying relations.

 

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