Let A = {1, 2, 3}. The relation R on set A is | vedclass

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

Question

(A) $1$. Reflexivity: Since $(1, 1), (2, 2), (3, 3) \in R$,the relation $R$ is reflexive.$2$. Symmetry: We observe that $(1, 2) \in R$,but $(2, 1) 
o

Vedclass · Accepted Answer

Reflexive but not symmetric

Vedclass · Answer

(A) $1$. Reflexivity: Since $(1, 1), (2, 2), (3, 3) \in R$,the relation $R$ is reflexive.$2$. Symmetry: We observe that $(1, 2) \in R$,but $(2, 1) 
otin R$. Therefore,$R$ is not symmetric.$3$. Transitivity: For any $(a, b) \in R$ and $(b, c) \in R$,we check if $(a, c) \in R$. - $(1, 2) \in R$ and $(2, 3) \in R \implies (1, 3) \in R$ (which is present).- All other pairs satisfy the condition. Thus,$R$ is transitive.Conclusion: The relation $R$ is reflexive and transitive,but not symmetric.

Let $A = \{1, 2, 3\}$. The relation $R$ on set $A$ is defined as $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)\}$. Determine the nature of the relation $R$.

Similar Questions

Let $R$ be a relation from the set $\{1, 2, 3, \ldots, 60\}$ to itself such that $R = \{(a, b) : b = pq\}$,where $p, q \geq 3$ are prime numbers and $b \leq 60$. Then,the number of elements in $R$ is.

Consider set $A = \{1, 2, 3\}$. The number of symmetric relations that can be defined on $A$ containing the ordered pairs $(1, 2)$ and $(2, 1)$ is:

Let $R = \{(3, 3), (5, 5), (9, 9), (12, 12), (5, 12), (3, 9), (3, 12), (3, 5)\}$ be a relation on the set $A = \{3, 5, 9, 12\}.$ Then,$R$ is

Determine whether the following relation is reflexive,symmetric,and transitive:
Relation $R$ in the set $N$ of natural numbers defined as
$R = \{(x, y) : y = x + 5 \text{ and } x < 4\}$

Let the relation $R_1$ be defined by $R_1 = \{ (a, b) | a \ge b, a, b \in R \}$. Then $R_1$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module