Which Table Represents The Same Relation As The Set { ( − 6 , 4 ) , ( − 4 , 0 ) , ( − 3 , 2 ) , ( − 1 , 2 ) } \{(-6,4), (-4,0), (-3,2), (-1,2)\} {( − 6 , 4 ) , ( − 4 , 0 ) , ( − 3 , 2 ) , ( − 1 , 2 )} ?1. ${ \begin{tabular}{|c|c|} \hline X X X & Y Y Y \ \hline -6 & -3 \ \hline 4 & 2 \ \hline -4 & -1 \ \hline 0 & 2 \ \hline \end{tabular} }$2.

Introduction

In mathematics, a relation is a set of ordered pairs that describe a connection between two variables. Given a set of ordered pairs, we can represent it as a table, where each ordered pair is a row in the table. In this article, we will explore which table represents the same relation as the given set $\{(-6,4), (-4,0), (-3,2), (-1,2)\}$.

Understanding the Given Set

The given set is $\{(-6,4), (-4,0), (-3,2), (-1,2)\}$. This set consists of four ordered pairs, where each ordered pair represents a connection between two variables, $x$ and $y$. The values of $x$ and $y$ in each ordered pair are:

• $(-6,4)$: $x = -6$ and $y = 4$
• $(-4,0)$: $x = -4$ and $y = 0$
• $(-3,2)$: $x = -3$ and $y = 2$
• $(-1,2)$: $x = -1$ and $y = 2$

Analyzing the First Table

The first table is:

Let's analyze this table to see if it represents the same relation as the given set. We can start by comparing the values of $x$ and $y$ in each ordered pair.

• For the first ordered pair, $x = -6$ and $y = -3$, which is not in the given set.
• For the second ordered pair, $x = 4$ and $y = 2$, which is in the given set.
• For the third ordered pair, $x = -4$ and $y = -1$, which is not in the given set.
• For the fourth ordered pair, $x = 0$ and $y = 2$, which is in the given set.

As we can see, the first table does not represent the same relation as the given set, since it contains ordered pairs that are not in the given set.

Analyzing the Second Table

The second table is:

Let's analyze this table to see if it represents the same relation as the given set. We can start by comparing the values of $x$ and $y$ in each ordered pair.

• For the first ordered pair, $x = -6$ and $y = 4$, which is in the given set.
• For the second ordered pair, $x = -4$ and $y = 0$, which is in the given set.
• For the third ordered pair, $x = -3$ and $y = 2$, which is in the given set.
• For the fourth ordered pair, $x = -1$ and $y = 2$, which is in the given set.

As we can see, the second table represents the same relation as the given set, since it contains all the ordered pairs in the given set.

Conclusion

In conclusion, the second table represents the same relation as the given set $\{(-6,4), (-4,0), (-3,2), (-1,2)\}$. This is because the second table contains all the ordered pairs in the given set, while the first table does not.

Final Answer

Q: What is a relation in mathematics?

A: A relation in mathematics is a set of ordered pairs that describe a connection between two variables. It is a way to represent a connection between two sets of values.

Q: How is a relation represented in a table?

A: A relation is represented in a table by listing the ordered pairs as rows in the table. Each ordered pair is a row in the table, with the values of the two variables in the pair listed in separate columns.

Q: What is the difference between a relation and a function?

A: A relation is a set of ordered pairs that describe a connection between two variables, while a function is a special type of relation where each value of the first variable (the input) is associated with exactly one value of the second variable (the output).

Q: How do I determine if two tables represent the same relation?

A: To determine if two tables represent the same relation, you need to compare the ordered pairs in each table. If the tables contain the same ordered pairs, then they represent the same relation.

Q: What is the significance of the given set $\{(-6,4), (-4,0), (-3,2), (-1,2)\}$?

A: The given set $\{(-6,4), (-4,0), (-3,2), (-1,2)\}$ is a set of ordered pairs that describe a connection between two variables, $x$ and $y$. It is used to represent a relation in mathematics.

Q: How do I analyze a table to determine if it represents the same relation as a given set?

A: To analyze a table to determine if it represents the same relation as a given set, you need to compare the ordered pairs in the table with the ordered pairs in the given set. If the table contains all the ordered pairs in the given set, then it represents the same relation.

Q: What is the final answer to the problem of determining which table represents the same relation as the given set?

A: The final answer to the problem of determining which table represents the same relation as the given set is 2. This is because the second table contains all the ordered pairs in the given set, while the first table does not.

Q: What is the significance of the second table in representing the same relation as the given set?

A: The second table is significant because it contains all the ordered pairs in the given set, making it a correct representation of the same relation.

Q: How can I apply the concept of relations to real-world problems?

A: The concept of relations can be applied to real-world problems in various ways, such as:

• Modeling the relationship between two variables in a data set
• Describing the connection between two sets of values
• Representing a function or a relation in a table or graph

Q: What are some common applications of relations in mathematics?

A: Some common applications of relations in mathematics include:

• Algebra: Relations are used to represent functions and equations
• Geometry: Relations are used to describe the connection between points and lines
• Calculus: Relations are used to represent functions and their derivatives

Q: How can I learn more about relations in mathematics?

A: You can learn more about relations in mathematics by:

• Reading textbooks and online resources
• Practicing problems and exercises
• Watching video tutorials and lectures
• Joining online communities and forums