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Question: Answered & Verified by Expert
Let $\mathrm{P}=\{1,2,3\}$ and a relation on set $\mathrm{P}$ is given by the set $\mathrm{R}=\{(1,2),(1,3),(2,1),(1,1),(2,2),(3,3),(2,3)\}$. Then $\mathrm{R}$ is
MathematicsSets and RelationsNDANDA 2012 (Phase 2)
Options:
  • A Reflexive, transitive but not symmetric
  • B Symmetric, transitive but notreflexive
  • C Symmetric, reflexive but not transitive
  • D None of the above
Solution:
2644 Upvotes Verified Answer
The correct answer is: Reflexive, transitive but not symmetric
Given relation $\mathrm{R}=\{(1,2),(1,3),(2,1),(1,1),(2,2),(3,3),(2,3)\}$ is
reflexive and transitive only but not symmetric $\because(3,1)$ and $(3,2) \notin \mathrm{R}$

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