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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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
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
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 )