Can we see this question from propositional logic point of view?

$\text{R be a Symmetric and Transitive relation on a set A }$ $\implies$ $\text{R is Reflexive & Equivalence relation}$

which is completely false.

It would be true if

$\text{R be a Reflexive, Symmetric and Transitive relation on a set A }$ $\implies$ $\text{Equivalence relation}$

$\text{R be a Symmetric and Transitive relation on a set A }$ $\implies$ $\text{R is Reflexive & Equivalence relation}$

which is completely false.

It would be true if

$\text{R be a Reflexive, Symmetric and Transitive relation on a set A }$ $\implies$ $\text{Equivalence relation}$