How does HashSet not allow duplicates?

Question

I was going through the add method of HashSet. It is mentioned that

If this set already contains the element, the call leaves t

Answer 1

public boolean add(E e) {
    return map.put(e, PRESENT)==null;
}

e is the key, So if e is already present put will not return null. Hence add will return false.

JavaDoc for put :

the previous value associated with key, or null if there was no mapping for key. (A null return can also indicate that the map previously associated null with key.)