diff --git a/Lib/test/test_dictviews.py b/Lib/test/test_dictviews.py
index 0cc6da3ba91..f90367660c5 100644
--- a/Lib/test/test_dictviews.py
+++ b/Lib/test/test_dictviews.py
@@ -85,6 +85,67 @@ class DictSetTest(unittest.TestCase):
         self.assertTrue(r == "dict_values(['ABC', 10])" or
                         r == "dict_values([10, 'ABC'])")
 
+    def test_keys_set_operations(self):
+        d1 = {'a': 1, 'b': 2}
+        d2 = {'b': 3, 'c': 2}
+        d3 = {'d': 4, 'e': 5}
+        self.assertEqual(d1.viewkeys() & d1.viewkeys(), {'a', 'b'})
+        self.assertEqual(d1.viewkeys() & d2.viewkeys(), {'b'})
+        self.assertEqual(d1.viewkeys() & d3.viewkeys(), set())
+        self.assertEqual(d1.viewkeys() & set(d1.viewkeys()), {'a', 'b'})
+        self.assertEqual(d1.viewkeys() & set(d2.viewkeys()), {'b'})
+        self.assertEqual(d1.viewkeys() & set(d3.viewkeys()), set())
+
+        self.assertEqual(d1.viewkeys() | d1.viewkeys(), {'a', 'b'})
+        self.assertEqual(d1.viewkeys() | d2.viewkeys(), {'a', 'b', 'c'})
+        self.assertEqual(d1.viewkeys() | d3.viewkeys(), {'a', 'b', 'd', 'e'})
+        self.assertEqual(d1.viewkeys() | set(d1.viewkeys()), {'a', 'b'})
+        self.assertEqual(d1.viewkeys() | set(d2.viewkeys()), {'a', 'b', 'c'})
+        self.assertEqual(d1.viewkeys() | set(d3.viewkeys()),
+                         {'a', 'b', 'd', 'e'})
+
+        self.assertEqual(d1.viewkeys() ^ d1.viewkeys(), set())
+        self.assertEqual(d1.viewkeys() ^ d2.viewkeys(), {'a', 'c'})
+        self.assertEqual(d1.viewkeys() ^ d3.viewkeys(), {'a', 'b', 'd', 'e'})
+        self.assertEqual(d1.viewkeys() ^ set(d1.viewkeys()), set())
+        self.assertEqual(d1.viewkeys() ^ set(d2.viewkeys()), {'a', 'c'})
+        self.assertEqual(d1.viewkeys() ^ set(d3.viewkeys()),
+                         {'a', 'b', 'd', 'e'})
+
+    def test_items_set_operations(self):
+        d1 = {'a': 1, 'b': 2}
+        d2 = {'a': 2, 'b': 2}
+        d3 = {'d': 4, 'e': 5}
+        self.assertEqual(
+            d1.viewitems() & d1.viewitems(), {('a', 1), ('b', 2)})
+        self.assertEqual(d1.viewitems() & d2.viewitems(), {('b', 2)})
+        self.assertEqual(d1.viewitems() & d3.viewitems(), set())
+        self.assertEqual(d1.viewitems() & set(d1.viewitems()),
+                         {('a', 1), ('b', 2)})
+        self.assertEqual(d1.viewitems() & set(d2.viewitems()), {('b', 2)})
+        self.assertEqual(d1.viewitems() & set(d3.viewitems()), set())
+
+        self.assertEqual(d1.viewitems() | d1.viewitems(),
+                         {('a', 1), ('b', 2)})
+        self.assertEqual(d1.viewitems() | d2.viewitems(),
+                         {('a', 1), ('a', 2), ('b', 2)})
+        self.assertEqual(d1.viewitems() | d3.viewitems(),
+                         {('a', 1), ('b', 2), ('d', 4), ('e', 5)})
+        self.assertEqual(d1.viewitems() | set(d1.viewitems()),
+                         {('a', 1), ('b', 2)})
+        self.assertEqual(d1.viewitems() | set(d2.viewitems()),
+                         {('a', 1), ('a', 2), ('b', 2)})
+        self.assertEqual(d1.viewitems() | set(d3.viewitems()),
+                         {('a', 1), ('b', 2), ('d', 4), ('e', 5)})
+
+        self.assertEqual(d1.viewitems() ^ d1.viewitems(), set())
+        self.assertEqual(d1.viewitems() ^ d2.viewitems(),
+                         {('a', 1), ('a', 2)})
+        self.assertEqual(d1.viewitems() ^ d3.viewitems(),
+                         {('a', 1), ('b', 2), ('d', 4), ('e', 5)})
+
+
+
 
 def test_main():
     test_support.run_unittest(DictSetTest)
diff --git a/Misc/NEWS b/Misc/NEWS
index 8d180ff1202..5c16eac84c1 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -28,6 +28,8 @@ Core and Builtins
 
 - Issue #7072: isspace(0xa0) is true on Mac OS X
 
+- Issue #8404: Fixed set operations on dictionary views.
+
 Library
 -------
 
diff --git a/Objects/dictobject.c b/Objects/dictobject.c
index be2517609ee..2ab15207f9f 100644
--- a/Objects/dictobject.c
+++ b/Objects/dictobject.c
@@ -3000,13 +3000,14 @@ static PyNumberMethods dictviews_as_number = {
 	0,				/*nb_add*/
 	(binaryfunc)dictviews_sub,	/*nb_subtract*/
 	0,				/*nb_multiply*/
+	0,				/*nb_divide*/
 	0,				/*nb_remainder*/
 	0,				/*nb_divmod*/
 	0,				/*nb_power*/
 	0,				/*nb_negative*/
 	0,				/*nb_positive*/
 	0,				/*nb_absolute*/
-	0,				/*nb_bool*/
+	0,				/*nb_nonzero*/
 	0,				/*nb_invert*/
 	0,				/*nb_lshift*/
 	0,				/*nb_rshift*/
@@ -3040,7 +3041,8 @@ PyTypeObject PyDictKeys_Type = {
 	PyObject_GenericGetAttr,		/* tp_getattro */
 	0,					/* tp_setattro */
 	0,					/* tp_as_buffer */
-	Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC,/* tp_flags */
+	Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC |
+		Py_TPFLAGS_CHECKTYPES,		/* tp_flags */
  	0,					/* tp_doc */
  	(traverseproc)dictview_traverse,	/* tp_traverse */
  	0,					/* tp_clear */
@@ -3124,7 +3126,8 @@ PyTypeObject PyDictItems_Type = {
 	PyObject_GenericGetAttr,		/* tp_getattro */
 	0,					/* tp_setattro */
 	0,					/* tp_as_buffer */
-	Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC,/* tp_flags */
+	Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC |
+		Py_TPFLAGS_CHECKTYPES,		/* tp_flags */
  	0,					/* tp_doc */
  	(traverseproc)dictview_traverse,	/* tp_traverse */
  	0,					/* tp_clear */