I'm not sure i understand you well, but...
Assuming that you want to find students which are not in
ClassInformation
table.
var result = studententities.Student
.Where(s => s.ID==some_id)
.Select(s => s.Name)
.Except(studententities.ClassInformation
.Select(ci => ci.Name)
.ToList();
foreach(string sname in result)
{
Console.WriteLine(sname);
}