Is it possible that TreeSet equals HashSet but not HashSet equals TreeSet

I had a interview today and the person taking my interview puzzled me with his statement asking if it possible that TreeSet equals HashSet but not HashSet equals TreeSet. I said “no” but according to him the answer is “yes”.

How is it even possible?

Answer

Your interviewer is right, they do not hold equivalence relation for some specific cases. It is possible that TreeSet can be equal to HashSet and not vice-versa. Here is an example:

TreeSet<String> treeSet = new TreeSet<>(String.CASE_INSENSITIVE_ORDER);
HashSet<String> hashSet = new HashSet<>();
treeSet.addAll(List.of("A", "b"));
hashSet.addAll(List.of("A", "B"));
System.out.println(hashSet.equals(treeSet)); // false
System.out.println(treeSet.equals(hashSet)); // true

The reason for this is that a TreeSet uses comparator to determine if an element is duplicate while HashSet uses equals.

Quoting TreeSet:

Note that the ordering maintained by a set (whether or not an explicit comparator is provided) must be consistent with equals if it is to correctly implement the Set interface.