If R is an equivalence relation on a set A,th | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) An equivalence relation $R$ on a set $A$ is reflexive,symmetric,and transitive.$1$. Reflexive: Since $(a, a) \in R$ for all $a \in A$,then $(a, a)

Vedclass · Accepted Answer

Equivalence

Vedclass · Answer

(C) An equivalence relation $R$ on a set $A$ is reflexive,symmetric,and transitive.$1$. Reflexive: Since $(a, a) \in R$ for all $a \in A$,then $(a, a) \in R^{-1}$,so $R^{-1}$ is reflexive.$2$. Symmetric: If $(a, b) \in R^{-1}$,then $(b, a) \in R$. Since $R$ is symmetric,$(a, b) \in R$,which implies $(b, a) \in R^{-1}$. Thus,$R^{-1}$ is symmetric.$3$. Transitive: If $(a, b) \in R^{-1}$ and $(b, c) \in R^{-1}$,then $(b, a) \in R$ and $(c, b) \in R$. Since $R$ is transitive,$(c, a) \in R$,which implies $(a, c) \in R^{-1}$. Thus,$R^{-1}$ is transitive.Since $R^{-1}$ is reflexive,symmetric,and transitive,it is an equivalence relation.

If $R$ is an equivalence relation on a set $A$,then $R^{-1}$ is

Similar Questions

With which of the following does hydrogen combine directly?

For all values of $a$ and $b$,the line $(a+2b)x + (a-b)y + (a+5b) = 0$ passes through a fixed point. Find that point.

The $pH$ of $0.1 \ M$ solution of the following salts increases in the order

Which of the following statements is wrong for viroids?

The bromine atom possesses $35$ electrons. It contains $6$ electrons in $2p$ orbital,$6$ electrons in $3p$ orbital and $5$ electrons in $4p$ orbital. Which of these electrons experiences the lowest effective nuclear charge?

Vedclass Test Series

Exam Paper Generator

Online Exam Module