In: Advanced Math
Determine if there exist a nonempty set S with operation ⋆ on S and a nonempty set S′ ⊂ S, which is closed with respect to ⋆, satisfying the following properties.
1) S has identity e with respect to ⋆. ′
2) e ∈/ S .
3) S′ has an identity with respect to ⋆.