diff --git a/pymysqlreplication/gtid.py b/pymysqlreplication/gtid.py
index 16d02a7c..2d149a4a 100644
--- a/pymysqlreplication/gtid.py
+++ b/pymysqlreplication/gtid.py
@@ -287,6 +287,8 @@ def merge_gtid(self, gtid):
         self.gtids = new_gtids
 
     def __contains__(self, other):
+        if isinstance(other, GtidSet):
+            return all(other_gtid in self.gtids for other_gtid in other.gtids)
         if isinstance(other, Gtid):
             return any(other in x for x in self.gtids)
         raise NotImplementedError
@@ -296,6 +298,13 @@ def __add__(self, other):
             new = GtidSet(self.gtids)
             new.merge_gtid(other)
             return new
+
+        if isinstance(other, GtidSet):
+            new = GtidSet(self.gtids)
+            for gtid in other.gtids:
+                new.merge_gtid(gtid)
+            return new
+
         raise NotImplementedError
 
     def __str__(self):