AIEEE

Explanation To determine the properties of the relation $R$, we need to check for reflexivity, symmetry, and transitivity. Reflexivity: A relation is reflexive if $(a, a) \in R$ for all $a \in A$. Since $(3, 3), (6, 6), (9, 9),$ and $(12, 12)$ are all in $R$, the relation is reflexive. Symmetry: A relation is symmetric if whenever $(a, b) \in R$, then $(b, a) \in R$. We have $(6, 12) \in R$, but $(12, 6) \notin R$. Thus, the relation is not symmetric. Transitivity: A relation is transitive if whenever $(a, b) \in R$ and $(b, c) \in R$, then $(a, c) \in R$. We have $(3, 6) \in R$ and $(6, 12) \in R$, and $(3, 12) \in R$. Also, $(3, 6) \in R$ and $(6, 6) \in R$, and $(3, 6) \in R$. The relation appears to be transitive. Therefore, the relation $R$ is reflexive and transitive, but not symmetric. So, the correct answer is Option D: $R$ is reflexive and transitive only.