Implementing composite in Java using Generics/Interface

Question

I have this simple example:

public class Imap {
    private Responder responder;

    public Imap(){
        this.responder = new Responder(this);
    }

    public void startService(){
        responder.doStuff();
    }

    public boolean supportsMe(){
        return true;
    }
}

public class Udp {
    private Responder responder;

    public Udp(){
        this.responder = new Responder(this);
    }

    public void startService(){
        responder.doStuff();
    }

    public boolean supportsMe(){
        return false;
    }
}

public class Responder {
    Object parent;

    public Responder(Object parent){
        this.parent = parent;
    }

    public void doStuff(){
        if(parent.supportsMe()){
            System.out.println("Parent supports me.");
        } else {
            System.out.println("Parent doesn't support me.");
        }
    }
}

The problem is supportsMe is undefined for Object. However, it is defined for both Udp and Imap. I would like Responder to be intelligent enough to call the right object. I believe the solution is to use Generics with Interface. I tried the following generic but still get a similar compile error (The method supportsMe() is undefined for the type T):

public class Responder<T> {
    T parent;

    public Responder(T parent){
        this.parent = parent;
    }

    public void doStuff(){
        if(parent.supportsMe()){
            System.out.println("Parent supports me.");
        } else {
            System.out.println("Parent doesn't support me.");
        }
    }
}

Any solutions to my problem?