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

Question

R is a relation on N given by R= (x, y): 4 x+3 y=20 . Which of the following belongs to R ? (A) (-4,12) (B) (5,0) (C) (3,4) (D) (2,4)

Tardigrade Admin · Accepted Answer

Since (-4,0) ∉ N and R is a relation on N, so, (-4,12),(5,0) ∉ R Now, 4(3)+3(4)=20 ⇒ 24=20, which is not true ∴ (3,4) ∉ R. Again, 4(2)+3(4)=20 ⇒ 20 =20, text which is true ∴ (2,4) ∈ R

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

$(- 4, 12)$

$(5, 0)$

$(3, 4)$

$(2, 4)$

Since $(- 4, 0) \in / N$ and $R$ is a relation on $N$ , so, $(- 4, 12), (5, 0) \in / R$
Now, $4 (3) + 3 (4) = 20 \Rightarrow 24 = 20$ , which is not true $∴ (3, 4) \in / R$ .
Again, $4 (2) + 3 (4) = 20$
$\Rightarrow 20 = 20, which is true$
$∴ (2, 4) \in R$

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

(−4,12)

(5,0)

(3,4)

(2,4)