JEE Main · 2005 · 08 May 2005 · Offline · Sets Relations and Functions

A relation is reflexive when every element is related to itself; here $(3,3)$, $(6,6)$, $(9,9)$ and $(12,12)$ are all present, so it is reflexive. For symmetry we would need the reverse of each pair, but $(3,6)$ belongs to the relation while $(6,3)$ does not, so it is not symmetric and therefore not an equivalence relation. Checking transitivity, every chain that can be formed, such as $(3,6)$ with $(6,12)$ requiring $(3,12)$, is completed by a pair already in the relation. The relation is thus reflexive and transitive only.