GATE | GATE CS 1999 | Question 51

[5 Marks question]

  1. Mr. X claims the following:
    If a relation R is both symmetric and transitive, then R is reflexive. For this, Mr. X offers the following proof-
    “From xRy, using symmetry we get yRy. Now because R is transitive, xRy and yRy together imply xRx. Therefore, R is reflexive.”
    Briefly point out the flaw in Mr. X’s proof.
  2. Give an example of relation R which is symmetric and transitive but not reflexive.



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