Let A = {1, 2, 3, 4} and R be a relation on A | vedclass

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

Question

(D) $1$. Reflexive: $A$ relation $R$ on set $A$ is reflexive if $(a, a) \in R$ for all $a \in A$. Here,$(1, 1), (2, 2), (3, 3), (4, 4) \in R$. Thus,$R

Vedclass · Accepted Answer

Both $A$ and $B$

Vedclass · Answer

(D) $1$. Reflexive: $A$ relation $R$ on set $A$ is reflexive if $(a, a) \in R$ for all $a \in A$. Here,$(1, 1), (2, 2), (3, 3), (4, 4) \in R$. Thus,$R$ is reflexive.$2$. Symmetric: $A$ relation $R$ is symmetric if $(a, b) \in R \implies (b, a) \in R$. - $(1, 2) \in R$ and $(2, 1) \in R$.- $(3, 1) \in R$ and $(1, 3) \in R$.- All other elements $(1, 1), (2, 2), (3, 3), (4, 4)$ are symmetric to themselves. Thus,$R$ is symmetric.$3$. Transitive: $A$ relation $R$ is transitive if $(a, b) \in R$ and $(b, c) \in R \implies (a, c) \in R$. - Consider $(3, 1) \in R$ and $(1, 2) \in R$. For $R$ to be transitive,$(3, 2)$ must be in $R$. However,$(3, 2) 
otin R$. Thus,$R$ is not transitive.Therefore,$R$ is both reflexive and symmetric.

Let $A = \{1, 2, 3, 4\}$ and $R$ be a relation on $A$,given by $R = \{(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (3, 1), (1, 3)\}$. Then $R$ is:

Similar Questions

Check whether the relation $R$ defined in the set $\{1, 2, 3, 4, 5, 6\}$ as $R = \{(a, b) : b = a + 1\}$ is reflexive,symmetric,or transitive.

The number of relations on the set $A = \{1, 2, 3\}$ containing $(1, 2)$ and $(2, 3)$, which are reflexive and transitive but not symmetric, is:

The number of symmetric relations defined on the set $\{1, 2, 3, 4\}$ which are not reflexive is

The number of reflexive relations on a set with $4$ elements is equal to

Let $L$ be the set of all straight lines in the Euclidean plane. Two lines $l_1$ and $l_2$ are said to be related by the relation $R$ if and only if $l_1$ is parallel to $l_2$. Then the relation $R$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module