 Solution

For EL with bottom, the eligible axioms are $\boxed{(2),(4),(5)}$. Axioms (1) and (3) contain universal restrictions, and (3) also contains a disjunction, so they are outside its syntax. For plain EL, whose constructors are $\top$, atomic names, conjunction and existential restriction, the eligible axioms are $\boxed{(2),(5)}$; (4) is excluded because it uses $\perp$. These conventions should not be conflated.

Here is a normalized TBox for the bottom-inclusive version. Introduce one fresh description logic concept $X$ for $\exists R.A$, and useThese are the usual normalized forms: an existential restriction on the left with an atomic right-hand side, an atomic left-hand side with an existential restriction on the right, or a conjunction of atomic names implying $\perp$. Here $\top$ is permitted as a filler.

The first two general concept inclusions force $X\equiv \exists R.A$. The third then says $\exists R.A⊑\exists R.\exists R.A$, exactly (2). Conversely, any model of (2) extends by $X=(\exists R.A{)}^{\mathcal{I}}$ to satisfy all three normalized general concept inclusions. The last two are the two directions of (5). For plain EL, delete just $A\sqcap B⊑\perp$ from this normalized TBox.