Given $R=\{(1,1),(2,2),(3,3),(1,2),(2,3)(1,3)\}$
$(1,1)(2,2)(3,3) \in R$
Hence $(a,a) \in$ R for $a \in \{1,2,3\}$
R is reflexive
$(1,2) \in R$ but $(2,1) \notin R$
R is not symmetric
$(1,2) \in R (2,3) \in R$ also $(1,3) \in R$
R is transitive
R is reflexive, transitive but not symmetric
Solution: 'A' option is correct