What is the correct way to check if a singleton instance has been instantiated or not?

I have seen the following two examples:

class singleton {
    protected:
        static singleton *instance;
        singleton() { }
    public:
        static singleton *getInstance() {
            if (instance == 0)
                instance = new singleton();
            return instance;
        }
};
singleton *singleton::instance = 0; //This seems weird - why isn't nullptr being used ?

And this example:

class Singleton
{
  private:

    static Singleton *p_inst;
    Singleton();

  public:

    static Singleton * instance()
    {
      if (!p_inst) // why isn't this being compared with nullptr ?
      {
        p_inst = new Singleton();
      }

      return p_inst;
    }
};

To check if the instance has been created, why don't people do something like this:

class Singleton
{
  private:

    static Singleton *p_inst = nullptr;
    Singleton();

  public:

    static Singleton * instance()
    {
      if (p_inst != nullptr) // why isn't this being compared with nullptr ?
      {
        p_inst = new Singleton();
      }

      return p_inst;
    }
};

What is the correct way ?