diff --git a/builtins/2.7/__builtin__.pyi b/builtins/2.7/__builtin__.pyi
index bdca135d6..5631691cf 100644
--- a/builtins/2.7/__builtin__.pyi
+++ b/builtins/2.7/__builtin__.pyi
@@ -539,28 +539,40 @@ class dict(MutableMapping[_KT, _VT], Generic[_KT, _VT]):
     def __str__(self) -> str: ...
 
 class set(MutableSet[_T], Generic[_T]):
-    @overload
-    def __init__(self) -> None: ...
-    @overload
-    def __init__(self, iterable: Iterable[_T]) -> None: ...
+    def __init__(self, iterable: Iterable[_T]=None) -> None: ...
     def add(self, element: _T) -> None: ...
-    def remove(self, element: _T) -> None: ...
-    def copy(self) -> AbstractSet[_T]: ...
-    def isdisjoint(self, s: AbstractSet[_T]) -> bool: ...
-    def issuperset(self, s: AbstractSet[_T]) -> bool: ...
-    def issubset(self, s: AbstractSet[_T]) -> bool: ...
-    def update(self, s: AbstractSet[_T]) -> None: ...
-    def difference_update(self, s: AbstractSet[_T]) -> None: ...
+    def clear(self) -> None: ...
+    def copy(self) -> set[_T]: ...
+    def difference(self, s: Iterable[Any]) -> set[_T]: ...
+    def difference_update(self, s: Iterable[Any]) -> None: ...
     def discard(self, element: _T) -> None: ...
-    def intersection_update(self, s: AbstractSet[_T]) -> None: ...
+    def intersection(self, s: Iterable[Any]) -> set[_T]: ...
+    def intersection_update(self, s: Iterable[Any]) -> None: ...
+    def isdisjoint(self, s: AbstractSet[Any]) -> bool: ...
+    def issubset(self, s: AbstractSet[Any]) -> bool: ...
+    def issuperset(self, s: AbstractSet[Any]) -> bool: ...
+    def pop(self) -> _T: ...
+    def remove(self, element: _T) -> None: ...
+    def symmetric_difference(self, s: Iterable[_T]) -> set[_T]: ...
+    def symmetric_difference_update(self, s: Iterable[_T]) -> None: ...
+    def union(self, s: Iterable[_T]) -> set[_T]: ...
+    def update(self, s: Iterable[_T]) -> None: ...
     def __len__(self) -> int: ...
     def __contains__(self, o: object) -> bool: ...
     def __iter__(self) -> Iterator[_T]: ...
     def __str__(self) -> str: ...
-    def __and__(self, s: AbstractSet[_T]) -> AbstractSet[_T]: ...
-    def __or__(self, s: AbstractSet[_S]) -> AbstractSet[Union[_T, _S]]: ...
-    def __sub__(self, s: AbstractSet[_T]) -> AbstractSet[_T]: ...
-    def __xor__(self, s: AbstractSet[_S]) -> AbstractSet[Union[_T, _S]]: ...
+    def __and__(self, s: AbstractSet[Any]) -> set[_T]: ...
+    def __iand__(self, s: AbstractSet[Any]) -> set[_T]: ...
+    def __or__(self, s: AbstractSet[_S]) -> set[Union[_T, _S]]: ...
+    def __ior__(self, s: AbstractSet[_S]) -> set[Union[_T, _S]]: ...
+    def __sub__(self, s: AbstractSet[Any]) -> set[_T]: ...
+    def __isub__(self, s: AbstractSet[Any]) -> set[_T]: ...
+    def __xor__(self, s: AbstractSet[_S]) -> set[Union[_T, _S]]: ...
+    def __ixor__(self, s: AbstractSet[_S]) -> set[Union[_T, _S]]: ...
+    def __le__(self, s: AbstractSet[Any]) -> bool: ...
+    def __lt__(self, s: AbstractSet[Any]) -> bool: ...
+    def __ge__(self, s: AbstractSet[Any]) -> bool: ...
+    def __gt__(self, s: AbstractSet[Any]) -> bool: ...
     # TODO more set operations
 
 class frozenset(AbstractSet[_T], Generic[_T]):
diff --git a/stdlib/2.7/typing.pyi b/stdlib/2.7/typing.pyi
index c5cc78fde..92d8d23e8 100644
--- a/stdlib/2.7/typing.pyi
+++ b/stdlib/2.7/typing.pyi
@@ -129,7 +129,6 @@ class AbstractSet(Sized, Iterable[_T_co], Generic[_T_co]):
     def __xor__(self, s: AbstractSet[_T]) -> AbstractSet[Union[_T_co, _T]]: ...
     # TODO: argument can be any container?
     def isdisjoint(self, s: AbstractSet[Any]) -> bool: ...
-    def union(self, s: AbstractSet[_T]) -> AbstractSet[Union[_T_co, _T]]: ...
 
 class MutableSet(AbstractSet[_T], Generic[_T]):
     @abstractmethod