diff --git a/src/sage/sets/set.py b/src/sage/sets/set.py
index b988525a880..c4e39fd3df7 100644
--- a/src/sage/sets/set.py
+++ b/src/sage/sets/set.py
@@ -1061,10 +1061,20 @@ def __richcmp__(self, other, op):
             False
             sage: Set([1]) == set([1])
             True
+
+        Test set equality and inequality::
+
+            sage: L = {0}
+            sage: S = Set(L)
+            sage: S == L
+            True
+            sage: S != L
+            False
         """
         if not isinstance(other, Set_object_enumerated):
             if isinstance(other, (set, frozenset)):
-                return self.set() == other
+                if self.set() == other:
+                    return rich_to_bool(op, 0)
             return NotImplemented
         if self.set() == other.set():
             return rich_to_bool(op, 0)