diff --git a/Lib/_abcoll.py b/Lib/_abcoll.py
index 0957553..a1b9b3c 100644
--- a/Lib/_abcoll.py
+++ b/Lib/_abcoll.py
@@ -209,7 +209,7 @@ class Set(Sized, Iterable, Container):
         return cls(it)
 
     def __and__(self, other):
-        if not isinstance(other, Iterable):
+        if not isinstance(other, Set):
             return NotImplemented
         return self._from_iterable(value for value in other if value in self)
 
@@ -220,26 +220,30 @@ class Set(Sized, Iterable, Container):
         return True
 
     def __or__(self, other):
-        if not isinstance(other, Iterable):
+        if not isinstance(other, Set):
             return NotImplemented
         chain = (e for s in (self, other) for e in s)
         return self._from_iterable(chain)
 
     def __sub__(self, other):
         if not isinstance(other, Set):
-            if not isinstance(other, Iterable):
-                return NotImplemented
-            other = self._from_iterable(other)
+            return NotImplemented
         return self._from_iterable(value for value in self
                                    if value not in other)
 
     def __xor__(self, other):
         if not isinstance(other, Set):
-            if not isinstance(other, Iterable):
-                return NotImplemented
-            other = self._from_iterable(other)
+            return NotImplemented
         return (self - other) | (other - self)
 
+    def __rsub__(self, other):
+        if not isinstance(other, Set):
+            return NotImplemented
+        return self._from_iterable(other) - self
+    __ror__ = __or__
+    __rand__ = __and__
+    __rxor__ = __xor__
+
     def _hash(self):
         """Compute the hash value of a set.
 
@@ -311,34 +315,40 @@ class MutableSet(Set):
         except KeyError:
             pass
 
-    def __ior__(self, it: Iterable):
-        for value in it:
+    def __ior__(self, other: Set):
+        if not isinstance(other, Set):
+            return NotImplemented
+        for value in other:
             self.add(value)
         return self
 
-    def __iand__(self, it: Iterable):
-        for value in (self - it):
+    def __iand__(self, other: Set):
+        if not isinstance(other, Set):
+            return NotImplemented
+        for value in (self - other):
             self.discard(value)
         return self
 
-    def __ixor__(self, it: Iterable):
-        if it is self:
+    def __ixor__(self, other: Set):
+        if not isinstance(other, Set):
+            return NotImplemented
+        if other is self:
             self.clear()
         else:
-            if not isinstance(it, Set):
-                it = self._from_iterable(it)
-            for value in it:
+            for value in other:
                 if value in self:
                     self.discard(value)
                 else:
                     self.add(value)
         return self
 
-    def __isub__(self, it: Iterable):
-        if it is self:
+    def __isub__(self, other: Set):
+        if not isinstance(other, Set):
+            return NotImplemented
+        if other is self:
             self.clear()
         else:
-            for value in it:
+            for value in other:
                 self.discard(value)
         return self
 
diff --git a/Lib/test/test_collections.py b/Lib/test/test_collections.py
index 02b9dc3..7233cf6 100644
--- a/Lib/test/test_collections.py
+++ b/Lib/test/test_collections.py
@@ -476,6 +476,16 @@ class TestCollectionABCs(ABCTestCase):
                 return iter([])
         self.validate_comparison(MySet())
 
+    def test_set_interoperability(self):
+        # Classes inherited from MutableSet should interoperate with
+        # regular sets.  Issues #8743 and #2226.
+        w = WithSet('abracadabra')
+        s = set('simsalabim')
+        self.assertEqual(sorted(s&w), sorted(w&s))
+        self.assertEqual(sorted(s|w), sorted(w|s))
+        self.assertEqual(sorted(s^w), sorted(w^s))
+        self.assertEqual(sorted(s-w), sorted(WithSet(s) - set(w)))
+
     def test_hash_Set(self):
         class OneTwoThreeSet(Set):
             def __init__(self):