Symmetric and Transitive Relation is not necessarily Reflexive/Proof 1

Proof
Proof by Counterexample:

Let $S = \set {a, b, c}$.

Let:
 * $\alpha = \set {\tuple {a, a}, \tuple {a, b}, \tuple {b, a}, \tuple {b, b} }$

By inspection it is seen that $\alpha$ is both symmetric and transitive.

However, we have:
 * $\neg c \mathrel \alpha c$

Hence $\alpha$ is both symmetric and transitive but not reflexive.