Let ρ be a relation defined on N, the set of natural numbers, as �

1.	Let ρ be a relation defined on N, the set of natural numbers, as ρ = {(x, y) ∈ N × N : 2x + y = 41} Then (A) ρ is an equivalence relation (B) ρ is only reflexive relation (C) ρ is only symmetric relation (D) ρ is not transitive
Answer» The correct option (D) ρ is not transitive Explanation: ρ = {(x, y) ∈ N × N, 2x + y = 41} for reflexive relation x R x ⇒ 2x + x = 41 ⇒ x = 41/3 ∈ N for symmetric ⇒ x R y ⇒ 2x + y = 41 ≠ y R x (Not symmetric) for transitive xRy ⇒ 2x + y = 41 and yRz ⇒ 2y + z = 41, xRz (not transitive )

Let ρ be a relation defined on N, the set of natural numbers, as ρ = {(x, y) ∈ N × N : 2x + y = 41} Then (A) ρ is an equivalence relation (B) ρ is only reflexive relation (C) ρ is only symmetric relation (D) ρ is not transitive

Answer»

The correct option (D) ρ is not transitive

Explanation:

ρ = {(x, y) ∈ N × N, 2x + y = 41}

for reflexive relation x R x ⇒ 2x + x = 41 ⇒ x = 41/3 ∈ N

for symmetric ⇒ x R y ⇒ 2x + y = 41 ≠ y R x (Not symmetric)

for transitive xRy ⇒ 2x + y = 41 and yRz ⇒ 2y + z = 41, xRz (not transitive )

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Let ρ be a relation defined on N, the set of natural numbers, as ρ = {(x, y) ∈ N × N : 2x + y = 41} Then (A) ρ is an equivalence relation (B) ρ is only reflexive relation (C) ρ is only symmetric relation (D) ρ is not transitive

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