Q162 / 270 · NDA 2012 (Phase 2) · Mathematics

Let $P=\{1,2,3\}$ and a relation on set $P$ is given by the set $R=\{(1,2),(1,3),(2,1),(1,1),(2,2),(3,3),(2,3)\}$. Then R is :

  • A
    Reflexive, transitive but not symmetric
  • B
    Symmetric, transitive but not reflexive
  • Correct answer
    C
    Symmetric, reflexive but not transitive
  • D
    None of the above

Solution

$\because \mathrm{R}=\{(1,2),(1,3),(2,1),(1,1),(2,2),(3,3),(2,3)\}$ Relation is reflexive $\because$ it contains $(1,1),(2,2),(3,3)$, symmetric $\because(1,2)(2,1)$ hence relation is symmetric, reflexive but not transitive.

Hence, the correct answer is option: 'C'.

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