Determine the properties of set relations such as reflexivity, symmetry, transitivity, and more.
The set S can be defined as: $$ S = \{1, 2, 3, 4\} $$
The relation R can be expressed as: $$ R = \{(1, 2), (1, 3), (2, 4), (3, 4)\} $$
A relation is reflexive if: $$ \forall a \in S, \ (a, a) \in R $$
A relation is symmetric if: $$ \forall a, b \in S, \ (a, b) \in R \implies (b, a) \in R $$
A relation is transitive if: $$ \forall a, b, c \in S, \ (a, b) \in R \text{ and } (b, c) \in R \implies (a, c) \in R $$