R is a relation on mathbb{N} given by R={(x, | vedclass

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

Question

(D) Given the relation $R = \{(x, y) : 4x + 3y = 20\}$ on the set of natural numbers $\mathbb{N}$.For $(x, y) \in R$,both $x$ and $y$ must be natural

Vedclass · Accepted Answer

$(2, 4)$

Vedclass · Answer

(D) Given the relation $R = \{(x, y) : 4x + 3y = 20\}$ on the set of natural numbers $\mathbb{N}$.For $(x, y) \in R$,both $x$ and $y$ must be natural numbers (i.e.,$x, y \in \{1, 2, 3, \dots\}$).Let us check the options:$(a)$ $(-4, 12)$: $-4 
otin \mathbb{N}$.$(b)$ $(5, 0)$: $0 
otin \mathbb{N}$.$(c)$ $(3, 4)$: $4(3) + 3(4) = 12 + 12 = 24 
eq 20$.$(d)$ $(2, 4)$: $4(2) + 3(4) = 8 + 12 = 20$. Since $2 \in \mathbb{N}$ and $4 \in \mathbb{N}$,$(2, 4) \in R$.Thus,the correct option is $(d)$.

$R$ is a relation on $\mathbb{N}$ given by $R=\{(x, y): 4x+3y=20\}$. Which of the following belongs to $R$?

Similar Questions

In the context of a power set containing a subset,the relation 'is a subset of' $(\subseteq)$ is:

Let $A = \{1, 2, 3, 4, 5, 6\}$. Define a relation $R$ from $A$ to $A$ by $R = \{(x, y) : y = x + 1\}$. Depict this relation using an arrow diagram.

Let $A = \{1, 2, 3, 4\}$,$B = \{1, 5, 9, 11, 15, 16\}$,and $f = \{(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)\}$. Is $f$ a relation from $A$ to $B$? Justify your answer.

$A$ relation from $P$ to $Q$ is

Let the number of elements of the sets $A$ and $B$ be $p$ and $q$, respectively. Then, the number of relations from the set $A$ to the set $B$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module