bpo-38248: Fix inconsistent immediate asyncio.Task cancellation (GH-16330)

diff --git a/Lib/asyncio/tasks.py b/Lib/asyncio/tasks.py
index a0cb884..38d9827 100644
--- a/Lib/asyncio/tasks.py
+++ b/Lib/asyncio/tasks.py
@@ -284,7 +284,7 @@
             if self._must_cancel:
                 # Task is cancelled right before coro stops.
                 self._must_cancel = False
-                super().set_exception(exceptions.CancelledError())
+                super().cancel()
             else:
                 super().set_result(exc.value)
         except exceptions.CancelledError:
diff --git a/Lib/test/test_asyncio/test_tasks.py b/Lib/test/test_asyncio/test_tasks.py
index 576714f..dde84b8 100644
--- a/Lib/test/test_asyncio/test_tasks.py
+++ b/Lib/test/test_asyncio/test_tasks.py
@@ -604,9 +604,11 @@
             return 12
 
         t = self.new_task(loop, task())
+        self.assertFalse(t.cancelled())
         self.assertRaises(
             asyncio.CancelledError, loop.run_until_complete, t)
         self.assertTrue(t.done())
+        self.assertTrue(t.cancelled())
         self.assertFalse(t._must_cancel)  # White-box test.
         self.assertFalse(t.cancel())
 
@@ -621,9 +623,11 @@
             return 12
 
         t = self.new_task(loop, task())
+        self.assertFalse(t.cancelled())
         self.assertRaises(
             asyncio.CancelledError, loop.run_until_complete, t)
         self.assertTrue(t.done())
+        self.assertTrue(t.cancelled())
         self.assertFalse(t._must_cancel)  # White-box test.
         self.assertFalse(t.cancel())