Let $R=\{(3,3),(6,6),(9,9),(12,12),(6,12),(3,9),(3,12),(3,6)\}$ be a relation on the set $A=\{3,6,9,12\}$ .…

Let $R=\{(3,3),(6,6),(9,9),(12,12),(6,12),(3,9),(3,12),(3,6)\}$ be a relation on the set $A=\{3,6,9,12\}$ . The relation is
  1. reflexive and transitive only
  2. reflexive only
  3. an equivalence relation
  4. reflexive and symmetric only

Solution

Reflexive and transitive only. e.g. $(3,3),(6,6),(9,9),(12,12)$ [Reflexive] $(3,6),(6,12),(3,12)$ [Transitive].

Asked in: JEE Main 2005

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