diff --git a/Lib/test/test_sets.py b/Lib/test/test_sets.py
index 416b7cac3a0..1b26d4c82d8 100644
--- a/Lib/test/test_sets.py
+++ b/Lib/test/test_sets.py
@@ -1,6 +1,6 @@
 #!/usr/bin/env python
 
-import unittest, operator, copy, pickle
+import unittest, operator, copy, pickle, random
 from sets import Set, ImmutableSet
 from test import test_support
 
@@ -711,18 +711,18 @@ class TestCopyingNested(TestCopying):
 
 class TestIdentities(unittest.TestCase):
     def setUp(self):
-        self.a = Set('abracadabra')
-        self.b = Set('alacazam')
+        self.a = Set([random.randrange(100) for i in xrange(50)])
+        self.b = Set([random.randrange(100) for i in xrange(50)])
 
     def test_binopsVsSubsets(self):
         a, b = self.a, self.b
-        self.assert_(a - b < a)
-        self.assert_(b - a < b)
-        self.assert_(a & b < a)
-        self.assert_(a & b < b)
-        self.assert_(a | b > a)
-        self.assert_(a | b > b)
-        self.assert_(a ^ b < a | b)
+        self.assert_(a - b <= a)
+        self.assert_(b - a <= b)
+        self.assert_(a & b <= a)
+        self.assert_(a & b <= b)
+        self.assert_(a | b >= a)
+        self.assert_(a | b >= b)
+        self.assert_(a ^ b <= a | b)
 
     def test_commutativity(self):
         a, b = self.a, self.b
@@ -744,12 +744,19 @@ class TestIdentities(unittest.TestCase):
         self.assertEqual((a-b)|(b-a), a^b)
 
     def test_exclusion(self):
-        # check that inverse operations show non-overlap
+        # check that inverse operations do not overlap
         a, b, zero = self.a, self.b, Set()
         self.assertEqual((a-b)&b, zero)
         self.assertEqual((b-a)&a, zero)
         self.assertEqual((a&b)&(a^b), zero)
 
+    def test_cardinality_relations(self):
+        a, b = self.a, self.b
+        self.assertEqual(len(a), len(a-b) + len(a&b))
+        self.assertEqual(len(b), len(b-a) + len(a&b))
+        self.assertEqual(len(a^b), len(a-b) + len(b-a))
+        self.assertEqual(len(a|b), len(a-b) + len(a&b) + len(b-a))
+
 #==============================================================================
 
 libreftest = """