Name: Relations
Uploaded: 2019-07-19
Duration: 12 min 9 s
Description: In this video, we will learn about the relation in sets and the representation of relation by the set builder method, roster method, and arrow method.

Question

Let

A = {1, 2, 3}

, and let

R_{1} = \{(1, 1), (1, 3), (3, 1), (2, 2), (2, 1), (3, 3)\}, R_{2} = \{(2, 2), (3, 1), (1, 3)\}, R_{3} = \{(1, 3), (3, 3)\}

. Find whether or not each of the relations

R_{1} = \{(1, 1), (1, 3), (3, 1), (2, 2), (2, 1), (3, 3)\}, R_{2} = \{(2, 2), (3, 1), (1, 3)\}, R_{3} = \{(1, 3), (3, 3)\}

on

A

is

A = \{1, 2, 3\}

is reflexive, symmetric and transitive.

Accepted Answer

Consider $R_{1} = \{(1, 1), (1, 3), (3, 1), (2, 2), (2, 1), (3, 3)\}$
Here, $(1, 1), (2, 2), (3, 3) \in R_{1}$
So, $R_{1}$ is reflexive.
Here, $(2, 1) \in R_{1}$ , but $(1, 2) \notin R_{1}$
So, $A = \{1, 2, 3\}$ is not symmetric.
Here, $(2, 1) \in R_{1}$ and $(1, 3) \in R_{1}$ , but $(2, 3) \notin R_{1}$ .
So, $R_{1}$ is not transitive.

Consider $R_{2} = \{(2, 2), (3, 1), (1, 3)\}$
Clearly, $(1, 1)$ and $(3, 3) \notin R_{2}$
So, $R_{2}$ is not reflexive.
Here, $(1, 3) \in R_{2}$ and $(3, 1) \in R_{2}$
So, $R_{2}$ is symmetric.
Here, $(1, 3) \in R_{2}$ and $(3, 1) \in R_{2}$
But $(3, 3) \notin R_{2}$
So, $R_{2}$ is not transitive.

Consider $R_{3} = \{(1, 3), (3, 3)\}$
Clearly, $(1, 1) \notin R_{3}$
So, $R_{3}$ is not reflexive.
Here, $(1, 3) \in R_{3}$ , but $(3, 1) \notin R_{3}$
So, $R_{3}$ is not symmetric.
Here, $(1, 3) \in R_{3}$ and $(3, 3) \in R_{3}$
Also, $(1, 3) \in R_{3}$
So, $R_{3}$ is transitive.

Let $A = {1, 2, 3}$ , and let $R_{1} = \{(1, 1), (1, 3), (3, 1), (2, 2), (2, 1), (3, 3)\}, R_{2} = \{(2, 2), (3, 1), (1, 3)\}, R_{3} = \{(1, 3), (3, 3)\}$ . Find whether or not each of the relations $R_{1}, R_{2}, R_{3}$ on $A$ is $A = \{1, 2, 3\}$ is reflexive, symmetric and transitive.

Important Questions on Relation

Learn and Prepare for any exam you want !

Let A={1, 2, 3}, and let R1=(1, 1), (1, 3), (3, 1), (2, 2), (2, 1), (3, 3), R2=(2, 2), (3, 1), (1, 3), R3=(1, 3), (3, 3). Find whether or not each of the relations R1, R2, R3 on A is A=1, 2, 3 is reflexive, symmetric and transitive.

Important Questions on Relation

Learn and Prepare for any exam you want !

Let $A = {1, 2, 3}$ , and let $R_{1} = \{(1, 1), (1, 3), (3, 1), (2, 2), (2, 1), (3, 3)\}, R_{2} = \{(2, 2), (3, 1), (1, 3)\}, R_{3} = \{(1, 3), (3, 3)\}$ . Find whether or not each of the relations $R_{1}, R_{2}, R_{3}$ on $A$ is $A = \{1, 2, 3\}$ is reflexive, symmetric and transitive.