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Let be a relation defined onN, the set of natural numbers, as

Question

Let $ρ$ be a relation defined on $N$ , the set of natural numbers, as
$ρ = {(x, y) \in N \times N : 2 x + y = 41}$ then

ρ

is an equivalence relation

ρ

is only reflexive relation

ρ

is only symmetric relation

ρ

is not transitive

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Mila Discussed

Let

ρ

be a relation defined on

N

, the set of natural numbers, as

ρ = {(x, y) \in N \times N : 2 x + y = 41}

then

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Text solutionVerified

ρ = {(x, y) \in N \times N : 2 x + y = 41}

for reflexive relation

x R x \Rightarrow 2 x + x = 41 \Rightarrow x = \frac{41}{3} \in / N

for symmetric

\Rightarrow x R y \Rightarrow 2 x + y = 41 \neq = y R x

(Not symmetric)
for transitive

x R y \Rightarrow 2 x + y = 41

and

y R z \Rightarrow 2 y + z = 41, x

(Not transitive)

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Question Text	Let $ρ$ be a relation defined on $N$ , the set of natural numbers, as $ρ = {(x, y) \in N \times N : 2 x + y = 41}$ then
Answer Type	Text solution:1
Upvotes	150