Can HashSet contain null? How many nulls?

Yes — HashSet allows exactly one null element. That's because HashSet is backed by HashMap, which permits one null key. Adding null a second time returns false and leaves the set unchanged, just like adding any other duplicate.

Why One Null Works

HashMap special-cases null keys: they always hash to bucket 0 (via the internal hash(null) == 0 rule), bypassing the usual key.hashCode() call. Equality for null keys is checked by reference (==). Since HashSet.add(e) delegates to map.put(e, PRESENT), the same null-handling applies.

Set<String> s = new HashSet<>();
s.add(null);            // returns true — added
s.add(null);            // returns false — already present
s.add("a");
s.contains(null);       // true
s.size();               // 2

Contrast with the Other Sets

• LinkedHashSet — same as HashSet: one null allowed (backed by LinkedHashMap).
• TreeSet — no null allowed. Adding null throws NullPointerException because the tree must call compareTo on the new element, and null.compareTo(...) is impossible. (With a custom Comparator that tolerates null, you could in principle accept it, but the default naturalOrder won't.)
• Set.of(...) — null-hostile by design. Set.of(null) throws NPE at construction, and Set.of("a").contains(null) also throws NPE on lookup.
• ConcurrentHashMap-backed sets (e.g., ConcurrentHashMap.newKeySet()) — no null allowed, because null is used as a sentinel for "key absent" internally.

new TreeSet<String>().add(null);              // NullPointerException
Set.of("a", null);                            // NullPointerException
Set.of("a").contains(null);                   // NullPointerException
ConcurrentHashMap.<String>newKeySet().add(null); // NullPointerException

Why You Probably Shouldn't

Even where it's allowed, storing null in a Set is usually a code smell:

1. Stream pipelines break. stream().map(String::length) will NPE on a null element.
2. for-each is fragile. You constantly need null-guards inside the loop.
3. Set.of/Set.copyOf interop fails. You can't snapshot or transform via the modern immutable factories.
4. It hides intent. A null in a set of users probably means "missing" — model that explicitly with Optional or a sentinel.

The framework's null-hostility (visible in Set.of, ConcurrentHashMap, TreeSet) reflects the maintainers' position that allowing null was a Java 1.2 mistake they couldn't fix without breaking compatibility.