(A) \(R\) is reflexive and symmetric but not transitive. (B) \(R\) is reflexive and transitive but not symmetric. (C) \(R\) is symmetric and transitive but not reflexive. (D) \(R\) is an equivalence relation.

Want to ask us a question? Click here

Browse Questions

Ad |

0 votes

0 votes

- A relation R in a set A is a equivalance relation if it is symmetric, reflexive and transitive.
- A relation R in a set A is called $\mathbf{ reflexive},$ if $(a,a) \in R\;$ for every $\; a\in\;A$
- A relation R in a set A is called $\mathbf{symmetric}$, if $(a_1,a_2) \in R\;\Rightarrow\; (a_2,a_1)\in R \; for \;a_1,a_2 \in A$
- A relation R in a set A is called $\mathbf{transitive},$ if $(a_1,a_2) \in R$ and $(a_2,a_3) \in R \; \Rightarrow \;(a_1,a_3)\in R$ for all$\; a_1,a_2,a_3 \in A$

Given $R=\{(1,2),(2,2),(1,1),(4,4),(1,3),(3,3)(3,2)\}$ is the relation in the set $\{1,2,3,4\}$:

Given the set $\{1,2,3,4\}$, For every element of the set, $(1,1), (2,2), (3,3), (4,4) \in R$. Hence $R$ is reflexive.

Given the set $\{1,2,3,4\}$, we can observe that while $(1,2) \in R$, $(2,1) \not \in R$. Hence $R$ is not symmetric.

Given the set $\{1,2,3,4\}$, we can observe by looking at the ordered pairs that if $(a,b) \in R$ and $(b,c) \in R \rightarrow (a,c) \in R$.

Therefore, $R$ is transitive.

Therefore, $R$ is transitive and reflexive but not symmetric.

Ask Question

Take Test

x

JEE MAIN, CBSE, AIPMT Mobile and Tablet App

The ultimate mobile app to help you crack your examinations

...