Can I use objects in a database?

I have a case that I do not know which is the best structure of the relational database.

User

• ID
• Name

Task

• ID
• Name

I want the following conditions to be met

My solution was to put a new table called

Responsible

• ID
• Responsible (User.id)
• Who_assigns (User.id)
• Task (Task.id)

Then with programming I would perform a validation:

if( User.id == Responsable.Quien_asigna ) 
 TareasCreadasPorUsuario.AgregarTarea()


Mostrar(TareasCreadasPorUsuario); 

But, I was wondering if it would not be better, or if it was possible to put something like that better.

Task

• ID
• Name
• Responsible [Responsible, Who_assigns]

And at the end in programming

for(Responsable in Tarea.Responsables)
  if( User.id == Responsable.Quien_asigna ) 
     TareasCreadasPorUsuario.AgregarTarea()


Mostrar(TareasCreadasPorUsuario);