Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, | vedclass

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

Question

(C) Given $A = \{1, 2, 3, 4\}$ and $R = \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\}$.$1$. For $R$ to be symmetric,$(a, b) \in R$ must imply $(b, a) \in

Vedclass · Accepted Answer

Not symmetric

Vedclass · Answer

(C) Given $A = \{1, 2, 3, 4\}$ and $R = \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\}$.$1$. For $R$ to be symmetric,$(a, b) \in R$ must imply $(b, a) \in R$. Here,$(2, 3) \in R$ but $(3, 2) 
otin R$. Hence,$R$ is not symmetric.$2$. For $R$ to be reflexive,$(a, a) \in R$ for all $a \in A$. Since $(1, 1) 
otin R$,$R$ is not reflexive.$3$. For $R$ to be a function,each element in $A$ must have a unique image. Here,$2$ is mapped to both $4$ and $3$ (i.e.,$(2, 4) \in R$ and $(2, 3) \in R$),so $R$ is not a function.$4$. For $R$ to be transitive,$(a, b) \in R$ and $(b, c) \in R$ must imply $(a, c) \in R$. Here,$(1, 3) \in R$ and $(3, 1) \in R$,but $(1, 1) 
otin R$. Thus,$R$ is not transitive.Therefore,the correct statement is that $R$ is not symmetric.

Let $R = \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\}$ be a relation on the set $A = \{1, 2, 3, 4\}$. The relation $R$ is

Similar Questions

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

In the set $A = \{1, 2, 3, 4, 5\}$,a relation $R$ is defined by $R = \{(x, y) | x, y \in A \text{ and } x < y\}$. Then $R$ is

Show that the relation $R$ in the set $\{1, 2, 3\}$ given by $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)\}$ is reflexive but neither symmetric nor transitive.

The number of relations, defined on the set ${a, b, c, d}$, which are both reflexive and symmetric, is equal to:

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.

Vedclass Test Series

Exam Paper Generator

Online Exam Module