Let R = {(a, a)} be a relation on a set A. Th | vedclass

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

Question

(C) relation $R$ on a set $A$ is symmetric if $(x, y) \in R \implies (y, x) \in R$. Here,$R = \{(a, a)\}$. Since $(a, a) \in R$,its reverse $(a, a)$ i

Vedclass · Accepted Answer

Symmetric and antisymmetric

Vedclass · Answer

(C) relation $R$ on a set $A$ is symmetric if $(x, y) \in R \implies (y, x) \in R$. Here,$R = \{(a, a)\}$. Since $(a, a) \in R$,its reverse $(a, a)$ is also in $R$. Thus,$R$ is symmetric.$A$ relation $R$ is antisymmetric if $(x, y) \in R$ and $(y, x) \in R \implies x = y$. Here,if $(a, a) \in R$ and $(a, a) \in R$,then $a = a$,which is true. Thus,$R$ is antisymmetric.Therefore,$R$ is both symmetric and antisymmetric.

Let $R = \{(a, a)\}$ be a relation on a set $A$. Then $R$ is

Similar Questions

If $A = \{1, 2, 3, \dots, m\}$,then the total number of reflexive relations that can be defined from $A \to A$ is:

Let $R$ be a relation on $N \times N$ defined by $(a, b) R (c, d)$ if and only if $ad(b-c) = bc(a-d)$. Then $R$ is

Let $A = \{1, 2, 3\}$. The number of equivalence relations on $A$ containing $(1, 2)$ is . . . . . . .

Let $R$ be the relation in the set $N$ given by $R = \{(a, b) : a = b - 2, b > 6\}$. Choose the correct answer.

On the set of all real numbers,a relation $R$ is defined as $a \, R \, b$ if and only if $|a - b| \le 1$. Then $R$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module