diff --git a/src/FlagSetTrait.php b/src/FlagSetTrait.php
index 2865008..097bd34 100644
--- a/src/FlagSetTrait.php
+++ b/src/FlagSetTrait.php
@@ -143,6 +143,8 @@ public function __get($name)
 
     /**
      * Get a string representation of the flag set.
+     *
+     * @return string The string representation.
      */
     public function __toString()
     {
@@ -172,6 +174,89 @@ public function __set($name, $value)
         throw new LogicException('Flag-sets are immutable.');
     }
 
+    /**
+     * Compute the difference of flag-sets.
+     *
+     * @param self $other The other flag set to compare to.
+     *
+     * @return self A flag-set of the flags in $this and not in $other.
+     */
+    public function diff(self $other)
+    {
+        $result = new self();
+        foreach (self::$__flags as $flag) {
+            $result->{$flag} = $this->{$flag} && !$other->{$flag};
+        }
+
+        return $result;
+    }
+
+    /**
+     * Compute the symmetric difference of flag-sets.
+     *
+     * @param self $other The other flag set to compare to.
+     *
+     * @return self A flag-set of the flags in $this and not in $other, and vice versa.
+     */
+    public function symmetricDiff(self $other)
+    {
+        $result = new self();
+        foreach (self::$__flags as $flag) {
+            $result->{$flag} = $this->{$flag} !== $other->{$flag};
+        }
+
+        return $result;
+    }
+
+    /**
+     * Compute the intersection of flag-sets.
+     *
+     * @param self $other The other flag set to intersect with.
+     *
+     * @return self A flag-set of the flags in $this and $other.
+     */
+    public function intersect(self $other)
+    {
+        $result = new self();
+        foreach (self::$__flags as $flag) {
+            $result->{$flag} = $this->{$flag} && $other->{$flag};
+        }
+
+        return $result;
+    }
+
+    /**
+     * Compute the union of flag-sets.
+     *
+     * @param self $other The other flag set to union with.
+     *
+     * @return self A flag-set of the flags in $this or $other.
+     */
+    public function union(self $other)
+    {
+        $result = new self();
+        foreach (self::$__flags as $flag) {
+            $result->{$flag} = $this->{$flag} || $other->{$flag};
+        }
+
+        return $result;
+    }
+
+    /**
+     * Compute the inverse of this flag set.
+     *
+     * @return self The inverse of the flags in this flag-set.
+     */
+    public function inverse()
+    {
+        $result = new self();
+        foreach (self::$__flags as $flag) {
+            $result->{$flag} = !$this->{$flag};
+        }
+
+        return $result;
+    }
+
     private function __construct()
     {
         if (null === self::$__flags) {
diff --git a/test/suite/FlagSetTraitTest.php b/test/suite/FlagSetTraitTest.php
index 0bb728c..c7d1e3a 100644
--- a/test/suite/FlagSetTraitTest.php
+++ b/test/suite/FlagSetTraitTest.php
@@ -140,4 +140,142 @@ public function testToString()
             strval(TestFlags::defaults())
         );
     }
+
+    public function testDiff()
+    {
+        $defaults = TestFlags::defaults();
+
+        // diff to same
+        $flags = $defaults->diff(
+            $defaults
+        );
+        $this->assertFalse($flags->foo);
+        $this->assertFalse($flags->bar);
+        $this->assertFalse($flags->baz);
+        $this->assertFalse($flags->qux);
+
+        // diff to all
+        $flags = $defaults->diff(
+            TestFlags::all()
+        );
+        $this->assertFalse($flags->foo);
+        $this->assertFalse($flags->bar);
+        $this->assertFalse($flags->baz);
+        $this->assertFalse($flags->qux);
+
+        // diff to none
+        $flags = $defaults->diff(
+            TestFlags::none()
+        );
+        $this->assertTrue($flags->foo);
+        $this->assertFalse($flags->bar);
+        $this->assertTrue($flags->baz);
+        $this->assertFalse($flags->qux);
+    }
+
+    public function testSymmetricDiff()
+    {
+        $defaults = TestFlags::defaults();
+
+        // symmetric diff to same
+        $flags = $defaults->symmetricDiff(
+            $defaults
+        );
+        $this->assertFalse($flags->foo);
+        $this->assertFalse($flags->bar);
+        $this->assertFalse($flags->baz);
+        $this->assertFalse($flags->qux);
+
+        // symmetric diff to all
+        $flags = $defaults->symmetricDiff(
+            TestFlags::all()
+        );
+        $this->assertFalse($flags->foo);
+        $this->assertTrue($flags->bar);
+        $this->assertFalse($flags->baz);
+        $this->assertTrue($flags->qux);
+
+        // symmetric diff to none
+        $flags = $defaults->symmetricDiff(
+            TestFlags::none()
+        );
+        $this->assertTrue($flags->foo);
+        $this->assertFalse($flags->bar);
+        $this->assertTrue($flags->baz);
+        $this->assertFalse($flags->qux);
+    }
+
+    public function testIntersect()
+    {
+        $defaults = TestFlags::defaults();
+
+        // intersect to same
+        $flags = $defaults->intersect(
+            $defaults
+        );
+        $this->assertTrue($flags->foo);
+        $this->assertFalse($flags->bar);
+        $this->assertTrue($flags->baz);
+        $this->assertFalse($flags->qux);
+
+        // intersect to all
+        $flags = $defaults->intersect(
+            TestFlags::all()
+        );
+        $this->assertTrue($flags->foo);
+        $this->assertFalse($flags->bar);
+        $this->assertTrue($flags->baz);
+        $this->assertFalse($flags->qux);
+
+        // intersect to none
+        $flags = $defaults->intersect(
+            TestFlags::none()
+        );
+        $this->assertFalse($flags->foo);
+        $this->assertFalse($flags->bar);
+        $this->assertFalse($flags->baz);
+        $this->assertFalse($flags->qux);
+    }
+
+    public function testUnion()
+    {
+        $defaults = TestFlags::defaults();
+
+        // union to same
+        $flags = $defaults->union(
+            $defaults
+        );
+        $this->assertTrue($flags->foo);
+        $this->assertFalse($flags->bar);
+        $this->assertTrue($flags->baz);
+        $this->assertFalse($flags->qux);
+
+        // union to all
+        $flags = $defaults->union(
+            TestFlags::all()
+        );
+        $this->assertTrue($flags->foo);
+        $this->assertTrue($flags->bar);
+        $this->assertTrue($flags->baz);
+        $this->assertTrue($flags->qux);
+
+        // union to none
+        $flags = $defaults->union(
+            TestFlags::none()
+        );
+        $this->assertTrue($flags->foo);
+        $this->assertFalse($flags->bar);
+        $this->assertTrue($flags->baz);
+        $this->assertFalse($flags->qux);
+    }
+
+    public function testInverse()
+    {
+        $flags = TestFlags::defaults()->inverse();
+
+        $this->assertFalse($flags->foo);
+        $this->assertTrue($flags->bar);
+        $this->assertFalse($flags->baz);
+        $this->assertTrue($flags->qux);
+    }
 }