Index: Objects/setobject.c
===================================================================
--- Objects/setobject.c	(revision 84382)
+++ Objects/setobject.c	(working copy)
@@ -1171,6 +1171,31 @@
 
 PyDoc_STRVAR(clear_doc, "Remove all elements from this set.");
 
+/* Private helper function to check if the  */
+int
+isinstance_set_abc(PyObject *o)
+{
+	static PyObject *collections_set_abc = NULL;
+	PyObject *mod;
+
+	if (PyAnySet_Check(o))
+		return 1;
+	if (collections_set_abc == NULL) {
+		mod = PyImport_ImportModuleNoBlock("_abcoll");
+		if (mod == NULL) {
+			PyErr_Clear();
+			return 0;
+		}
+		collections_set_abc = PyObject_GetAttrString(mod, "Set");
+		if (collections_set_abc == NULL) {
+			Py_DECREF(mod);
+			PyErr_Clear();
+			return 0;
+		}
+	}
+	return PyObject_IsInstance(o, collections_set_abc);
+}
+
 static PyObject *
 set_union(PySetObject *so, PyObject *args)
 {
@@ -1204,7 +1229,7 @@
 {
     PySetObject *result;
 
-    if (!PyAnySet_Check(so) || !PyAnySet_Check(other)) {
+    if (!isinstance_set_abc(other)) {
         Py_INCREF(Py_NotImplemented);
         return Py_NotImplemented;
     }
@@ -1224,7 +1249,7 @@
 static PyObject *
 set_ior(PySetObject *so, PyObject *other)
 {
-    if (!PyAnySet_Check(other)) {
+    if (!isinstance_set_abc(other)) {
         Py_INCREF(Py_NotImplemented);
         return Py_NotImplemented;
     }
@@ -1377,7 +1402,7 @@
 static PyObject *
 set_and(PySetObject *so, PyObject *other)
 {
-    if (!PyAnySet_Check(so) || !PyAnySet_Check(other)) {
+    if (!isinstance_set_abc(other)) {
         Py_INCREF(Py_NotImplemented);
         return Py_NotImplemented;
     }
@@ -1389,7 +1414,7 @@
 {
     PyObject *result;
 
-    if (!PyAnySet_Check(other)) {
+    if (!isinstance_set_abc(other)) {
         Py_INCREF(Py_NotImplemented);
         return Py_NotImplemented;
     }
@@ -1604,7 +1629,7 @@
 static PyObject *
 set_sub(PySetObject *so, PyObject *other)
 {
-    if (!PyAnySet_Check(so) || !PyAnySet_Check(other)) {
+    if (!isinstance_set_abc(other)) {
         Py_INCREF(Py_NotImplemented);
         return Py_NotImplemented;
     }
@@ -1614,7 +1639,7 @@
 static PyObject *
 set_isub(PySetObject *so, PyObject *other)
 {
-    if (!PyAnySet_Check(other)) {
+    if (!isinstance_set_abc(other)) {
         Py_INCREF(Py_NotImplemented);
         return Py_NotImplemented;
     }
@@ -1708,7 +1733,7 @@
 static PyObject *
 set_xor(PySetObject *so, PyObject *other)
 {
-    if (!PyAnySet_Check(so) || !PyAnySet_Check(other)) {
+    if (!isinstance_set_abc(other)) {
         Py_INCREF(Py_NotImplemented);
         return Py_NotImplemented;
     }
@@ -1720,7 +1745,7 @@
 {
     PyObject *result;
 
-    if (!PyAnySet_Check(other)) {
+    if (!isinstance_set_abc(other)) {
         Py_INCREF(Py_NotImplemented);
         return Py_NotImplemented;
     }
Index: Lib/test/test_collections.py
===================================================================
--- Lib/test/test_collections.py	(revision 84382)
+++ Lib/test/test_collections.py	(working copy)
@@ -456,6 +456,16 @@
     # We should also test the proper behavior of the collection ABCs
     # as real base classes or mix-in classes.
 
+    def test_set_interoperability(self):
+        # classes inherited from MutableSet should interoperate with regular sets
+        # Issue #8743
+        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('simsalabim') - set('abracadabra')))
     def test_Set(self):
         for sample in [set, frozenset]:
             self.assertIsInstance(sample(), Set)