Why we can't use access modifier in the methods of class which implements two interfaces consist of same methods?

Question

public interface A
{
     void FirstDemo();
     void SecondDemo();
}
public interface B
{
     void FirstDemo();
     void SecondDemo();
}

 public class Demo : A, B
        {
            void A.FirstDemo()
            {
                Console.WriteLine("This is a function of first method of interface A");
            }
            void A.SecondDemo()
            {
                Console.WriteLine("This is a function of second method of interface A");
            }

            void B.FirstDemo()
            {
                Console.WriteLine("This is a function of first method of interface B");
            }
            void B.SecondDemo()
            {
                Console.WriteLine("This is a function of second method of interface B");
            }
        }

static void Main(string[] args)
        {
            A obj = new Demo();
            obj.SecondDemo();
            B obj1 = new Demo();
            obj1.FirstDemo();
        }

This program works properly. But my confusion is If I implement only one interface in the Demo class then I can give an access modifier in every method of that interface. But when I try to implement both interfaces (In this case: A and B) which consists same methods, within the same class (in this case: Demo class) then I'm not allowed to put public access modifier. why it happens?

Note : If I use single interface and implement it in Demo class, Then I can use access modifier to all methods which is declared in interface. So what's the issue in multiple interfaces with same methods ?

Answer 1

The distinction is not so much about "1 interface vs 2 interfaces", but rather "implicit vs explicit interface implementations". An explanation as for the "why is a visibility modifier forbidden" part of the question, I'll refer to question Why in C# does one need to mention the access modifier for implementation of an interface property?.

(Explicit interface implementations are implicitly public. Yes, you read that correctly.)

C# allows you to implement a single interface both implicitly and explicitly and they become different methods. The static type of the object determines which method to call:

interface IFace {
  void Method();
  void OnlyImplicit();
  void OnlyExplicit();
}

public class Obj : IFace {
  public void Method() {
    Console.WriteLine("implicit implementation");
  }

  void IFace.Method() {
    Console.WriteLine("explicit implementation");
  }

  public void OnlyImplicit() {
    Console.WriteLine("only implemented implicitly");
  }

  void IFace.OnlyExplicit() {
    Console.WriteLine("only implemented explicitly");
  }

  public void Main() {
    Obj o = new Obj(); // or: var o = new Obj();
    IFace i = o;

    o.Method(); // call of implicit impl
    i.Method(); // call of explicit impl

    o.OnlyImplicit(); // call of implicit impl
    i.OnlyImplicit(); // call of implicit impl

    i.OnlyExplicit(); // call of explicit impl

    // compile error, method is implemented explicitly,
    // can only be called when static type is interface;
    // cannot be called when static type is the class' type
    // (this is not so obvious):
    o.OnlyExplicit();
  }
}

Answer 2

In order to use an object you need an interface :-).

You can implement una interface implicitly and the other explicitly.

You can not provide multiple different implementations of the same interface method. Otherwise how the compiler will choice the implementation to use?

Suppose you implicit implements A and explicit B:

var demo = new Demo();
demo.FirstDemo(); // it uses public implementation (Demo class interface) that is A
var demoB = (B)demo;
demoB.FirstDemo(); // it uses B interface