Do you think children would have any class distinction if they have been let alone by their parents? Justify your answer.

For better or worse, I think that children will make distinctions based on something that could arguably be called class, even if "left alone" by their parents.  Children are products of evolution and environment.  However, "left alone" seems like a rather imprecise term we should look at first. 

Children can be left alone on a deserted island, as they are in Golding's Lord of the Flies, but I doubt that is what is meant in this context.  Certainly, very young children are not left alone to this degree most of the time. There is always some adult to watch over them, in the room or nearby.  I am going to assume that this term is meant to be about situations in which parents provide no overt cues to their children to suggest class differences, and really, that is usually the case, I think.

But children are astute little observers and learn quite early to notice differences in those around them and to discern attitudes on the part of their parents.  They may not consciously consider these differences, but they do absorb them. Some children are not invited over to play.  A mother has a frown of disapproval on her face as she looks upon a certain family in the neighborhood.  A father has a certain tone when he talks about a fellow worker.  If the family, nuclear and even extended, cares about class differences, a child's behavior and preferences will reflect that. During a child's teenage years, these preferences might be in the form of rebellious behavior, for instance, spending time with other teens from the wrong side of the tracks. 

You can see this reflected as children encounter one another at school.  Even when schools require uniforms, children find a way to make distinctions, with jewelry or shoes, for example.  Children are picked on for not being up to snuff with the latest iPhone or when picked up by an old Ford instead of a new Lexus. There is a competitive aspect to even after-school activities. Children are well aware of who gets to go to gymnastics, piano lessons, and dance class.  In the classroom, it is often painfully clear which children reap the benefits of books at home, art on the walls of their houses, and trips to the museum.  Children may not be able to articulate any of this very well, but they do know and they do judge.  There are at least as many cliques based on class as there are based on common interests.

Bear in mind that it is human to make some sort of distinctions.  We are evolutionarily primed to do so.  Recognition of "the other" saved many an early human group.  And wanting to be better than others is what motivates much human striving and accomplishment. That these differences are often class differences makes a great deal of sense in a way, since it combines protection against the threat of the other with motivation to excel. 

Be that as it may, we send our children to school to socialize and democratize them or at least we tell ourselves we do.  We expect them to be able to get along with others well, the whole All I Need to Know I Learned in Kindergarten (Fulghum) philosophy.  This has not always been successful, though, for any number of reasons, such as racial segregation and the segregation of physically or mentally disabled students.  Today, this democratization and socialization has new challenges in the ongoing effort to privatize public education.  To the degree that this is successful, children will become even more class-conscious, missing out on the irreplaceable experience of sitting in a classroom and a lunchroom with people who are not like them.

That there is no class division in America is a myth, I'm afraid. We have no formalization of class, as England or as India once did, but we have classes. And our children reflect this fact, even if we leave them to their own devices. We could solve this problem if we chose to, by searching our hearts and minds and working on, not tolerance for others, but respect and appreciation for others, modeling this for our children, and investing our time and energy in truly public education.