Let R be a relation on the set N defined by { | vedclass

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

Question

(D) The relation $R$ is defined on the set of natural numbers $N$ as $R = \{(x, y) : x, y \in N, 2x + y = 41\}$.$1$. Reflexivity: For $R$ to be reflex

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) The relation $R$ is defined on the set of natural numbers $N$ as $R = \{(x, y) : x, y \in N, 2x + y = 41\}$.$1$. Reflexivity: For $R$ to be reflexive,$(x, x)$ must be in $R$ for all $x \in N$. This implies $2x + x = 41$,so $3x = 41$,which gives $x = 41/3$. Since $41/3 
otin N$,the relation is not reflexive.$2$. Symmetry: For $R$ to be symmetric,if $(x, y) \in R$,then $(y, x)$ must be in $R$. We have $(1, 39) \in R$ because $2(1) + 39 = 41$. However,for $(39, 1)$ to be in $R$,we need $2(39) + 1 = 79$,which is not equal to $41$. Thus,$R$ is not symmetric.$3$. Transitivity: For $R$ to be transitive,if $(x, y) \in R$ and $(y, z) \in R$,then $(x, z)$ must be in $R$. We have $(1, 39) \in R$ and $(39, -37) 
otin N$. Since $y$ must be a natural number,we check pairs like $(1, 39)$ and $(20, 1)$. Here $(1, 39) \in R$ and $(20, 1) \in R$. For transitivity,$(1, 1)$ must be in $R$,but $2(1) + 1 = 3 
eq 41$. Thus,$R$ is not transitive.Therefore,$R$ is none of these.

Let $R$ be a relation on the set $N$ defined by $\{(x, y) | x, y \in N, 2x + y = 41\}$. Then $R$ is

Similar Questions

If $R$ is a relation from set $A$ to set $B$ and $S$ is a relation from set $B$ to set $C$,then the relation $S \circ R$ is:

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

Let $A = \{1, 2, 3, 4, 5\}$. $A$ relation $R$ on $A$ 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 $A = \{x \in Z : 0 \leq x \leq 12\},$ given by $R = \{(a, b) : |a - b| \text{ is a multiple of } 4\},$ is an equivalence relation. Find the set of all elements related to $1$.

The empty relation on a set $A$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module