PRESENT is just a dummy value -- the set doesn't really care what it is. What the set does care about is the map's keys. So the logic goes like this:
Set.add(a): map.put(a, PRESENT) // so far, this is just what you said the key "a" is in the map, so... keep the "a" key, but map its value to the PRESENT we just passed in also, return the old value (which we'll call OLD) look at the return value: it's OLD, != null. So return false.
Now, the fact that OLD == PRESENT doesn't matter -- and note that Map.put doesn't change the key, just the value mapped to that key. Since the map's keys are what the Set really cares about, the Set is unchanged.
In fact, there has been some change to the underlying structures of the Set -- it replaced a mapping of (a, OLD) with (a, PRESENT). But that's not observable from outside the Set's implementation. (And as it happens, that change isn't even a real change, since OLD == PRESENT).
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