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

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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

$(2, 4)$

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(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 $R$?

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