# Finding the Set of Ordered Triples of a Ternary Relation on A

• MHB
• trevor
In summary, a ternary relation is a mathematical concept that represents a relationship between three elements or objects. It can be defined as a subset of the Cartesian product A x A x A, and its purpose is to analyze and understand the relationship between the elements in a set in a systematic manner. The set of ordered triples of a ternary relation on A can be found by listing out all possible combinations or by using a table or diagram. Some real-life examples of ternary relations include the relationship between a student, a course, and a grade in a school, the relationship between a customer, a product, and a price in a store, and the relationship between a doctor, a patient, and a medication in a hospital.
trevor
Given that A = {1, 2, 3 ……..20} and R is a ternary relation on A defined by equation
x2 + 4y = z .Find the set of ordered triples of R.

trevor said:
Given that A = {1, 2, 3 ……..20} and R is a ternary relation on A defined by equation
x2 + 4y = z .Find the set of ordered triples of R.

spitballin' it ... hope I didn't miss any

(1,1,5), (1,2,9), (1,3,13), (1,4,17)

(2,1,8), (2,2,12), (2,3,16), (2,4,20)

(3,1,13), (3,2,17)

(4,1,20)

Too late... Posting anyway.

We need to find all triples $(x,y,z)$ such that $x^2+4y=z$ and $1\le x,y,z\le 20$. Let's do an exhaustive search.

$x=1,y=1\implies z=5$
$x=1,y=2\implies z=9$
$x=1,y=3\implies z=13$
$x=1,y=4\implies z=17$
$x=1,y=5\implies z=21$; this does not satisfy $z\le 20$.
$x=2,y=1\implies z=8$
$x=2,y=2\implies z=12$
$x=2,y=3\implies z=16$
$x=2,y=4\implies z=20$
$x=3,y=1\implies z=13$
$x=3,y=2\implies z=17$
$x=4,y=1\implies z=20$

Other values of $x$ and $y$ give $z$ that is greater than 20. So the set is
$R=\{(1,1,5),(1,2,9),(1,3,13),(1,4,17),(2,1,8),(2,2,12),(2,3,16),(2,4,20),(3,1,13),(3,2,17),(4,1,20)\}.$

For the future, please see https://mathhelpboards.com/rules/ 11 (click "Expand" in the beginning).

## 1. What is a ternary relation?

A ternary relation is a mathematical concept that represents a relationship between three elements or objects. It is a type of n-ary relation, where n refers to the number of elements involved in the relationship.

## 2. How do you define a ternary relation on a set A?

A ternary relation on a set A can be defined as a subset of the Cartesian product A x A x A, where each element in the subset is an ordered triple (a,b,c) such that a, b, and c are elements of set A.

## 3. What is the purpose of finding the set of ordered triples of a ternary relation on A?

The purpose of finding the set of ordered triples of a ternary relation on A is to analyze and understand the relationship between the elements of set A in a systematic and organized manner. It allows for a better understanding of the properties and characteristics of the ternary relation.

## 4. How do you find the set of ordered triples of a ternary relation on A?

To find the set of ordered triples of a ternary relation on A, you can list out all the possible combinations of elements from set A in the form of ordered triples. You can also use a table or diagram to represent the ternary relation and identify the ordered triples from it.

## 5. What are some real-life examples of ternary relations?

Some real-life examples of ternary relations include the relationship between a student, a course, and a grade in a school, the relationship between a customer, a product, and a price in a store, and the relationship between a doctor, a patient, and a medication in a hospital.

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