bpo-38716: stop rotating handlers from setting inherited namer and rotator to None (GH-17072)

diff --git a/Lib/test/test_logging.py b/Lib/test/test_logging.py
index 53b5bfc..6de8803 100644
--- a/Lib/test/test_logging.py
+++ b/Lib/test/test_logging.py
@@ -5030,6 +5030,25 @@
         self.assertFalse(os.path.exists(namer(self.fn + ".3")))
         rh.close()
 
+    def test_namer_rotator_inheritance(self):
+        class HandlerWithNamerAndRotator(logging.handlers.RotatingFileHandler):
+            def namer(self, name):
+                return name + ".test"
+
+            def rotator(self, source, dest):
+                if os.path.exists(source):
+                    os.rename(source, dest + ".rotated")
+
+        rh = HandlerWithNamerAndRotator(
+            self.fn, backupCount=2, maxBytes=1)
+        self.assertEqual(rh.namer(self.fn), self.fn + ".test")
+        rh.emit(self.next_rec())
+        self.assertLogFile(self.fn)
+        rh.emit(self.next_rec())
+        self.assertLogFile(rh.namer(self.fn + ".1") + ".rotated")
+        self.assertFalse(os.path.exists(rh.namer(self.fn + ".1")))
+        rh.close()
+
     @support.requires_zlib
     def test_rotator(self):
         def namer(name):