How are private:, protected:, and public: different?

All are from C++ faqs

The situation is similar to personal secrets (shared only with friends), family secrets (shared with friends and children), and nonsecrets (shared with anybody), respectively.

A private: member of a class is accessible only by members and friends of the class.

A protected: member of a class is accessible by members and friends of the class and by members and friends of derived classes, provided they access the base member via a pointer or a reference to their own derived class.

A public: member of a class is accessible by everyone.

class base{
private:
   int m;
protected:
   int i, j;
   void get(int c, int d){i=c; j=d;}
public:
   void set(int a, int b){i=a; j=b;}
};

class derived:public base{//protected, private
   int k;
public:
   void setk(){ k = i*j;}
};
   base b;
   derived d;
   b.i = 1; // wrong 
   d.i = 1; // wrong
   b.m = 2; // wrong
   d.k = 2; // wrong
   b.get(2,3); // wrong

   b.set(2,3); // OK
   d.set(3,4); // OK, wrong if using 'protected'
   d.setk();   // OK

base were inherited as private, then all members of base would become private members of derived. If base class is inherited as protected, all public and protected members of the base class become protected members of the derived class.

How can a class Y get the bits of an existing class X without making Y a kind-of X?

class X {
public:
 void f() throw();
 void g() throw();
private:
 int a_;
 float b_;
};
class Y1 {
public:
 void f() throw();
protected:
 X x_;                                             
};

void Y1::f() throw()
{ x_.f(); }