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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Sets and Relations

NTA Abhyas 2020 · Mathematics · Sets and Relations

The relation "less than" in the set of natural numbers is

The relation "less than" in the set of natural numbers is

Options

  1. Aonly symmetric
  2. Bonly transitive
  3. Conly reflexive
  4. Dan equivalence relation

Correct answer

B. only transitive

Step-by-step solution

Since, x<y,y<z⇒x<z∀x,y,z∈Nx < y, y < z ⇒ x < z \forall x, y, z \in \mathbb{N}

∴xRy,yRz⇒xRz∴xRy, yRz ⇒ xRz,

∴∴ Relation is transitive,

∵x<y∵x < y does not give y<xy < x,

∴∴ Relation is not symmetric.

Since, x<xx < x does not hold, hence the relation is not reflexive.
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