diff --git a/stdlib/2/__builtin__.pyi b/stdlib/2/__builtin__.pyi
index 0c476cec7..f64476f86 100644
--- a/stdlib/2/__builtin__.pyi
+++ b/stdlib/2/__builtin__.pyi
@@ -472,6 +472,30 @@ class bytearray(MutableSequence[int]):
 
 class bool(int):
     def __init__(self, o: object = ...) -> None: ...
+    @overload  # type: ignore
+    def __and__(self, x: bool) -> bool: ...
+    @overload  # type: ignore
+    def __and__(self, x: int) -> int: ...
+    @overload  # type: ignore
+    def __or__(self, x: bool) -> bool: ...
+    @overload  # type: ignore
+    def __or__(self, x: int) -> int: ...
+    @overload  # type: ignore
+    def __xor__(self, x: bool) -> bool: ...
+    @overload  # type: ignore
+    def __xor__(self, x: int) -> int: ...
+    @overload  # type: ignore
+    def __rand__(self, x: bool) -> bool: ...
+    @overload  # type: ignore
+    def __rand__(self, x: int) -> int: ...
+    @overload  # type: ignore
+    def __ror__(self, x: bool) -> bool: ...
+    @overload  # type: ignore
+    def __ror__(self, x: int) -> int: ...
+    @overload  # type: ignore
+    def __rxor__(self, x: bool) -> bool: ...
+    @overload  # type: ignore
+    def __rxor__(self, x: int) -> int: ...
 
 class slice(object):
     start = ...  # type: Optional[int]
diff --git a/stdlib/3/builtins.pyi b/stdlib/3/builtins.pyi
index f2cea0f93..74eb80635 100644
--- a/stdlib/3/builtins.pyi
+++ b/stdlib/3/builtins.pyi
@@ -537,6 +537,30 @@ class memoryview(Sized, Container[bytes]):
 
 class bool(int):
     def __init__(self, o: object = ...) -> None: ...
+    @overload  # type: ignore
+    def __and__(self, x: bool) -> bool: ...
+    @overload  # type: ignore
+    def __and__(self, x: int) -> int: ...
+    @overload  # type: ignore
+    def __or__(self, x: bool) -> bool: ...
+    @overload  # type: ignore
+    def __or__(self, x: int) -> int: ...
+    @overload  # type: ignore
+    def __xor__(self, x: bool) -> bool: ...
+    @overload  # type: ignore
+    def __xor__(self, x: int) -> int: ...
+    @overload  # type: ignore
+    def __rand__(self, x: bool) -> bool: ...
+    @overload  # type: ignore
+    def __rand__(self, x: int) -> int: ...
+    @overload  # type: ignore
+    def __ror__(self, x: bool) -> bool: ...
+    @overload  # type: ignore
+    def __ror__(self, x: int) -> int: ...
+    @overload  # type: ignore
+    def __rxor__(self, x: bool) -> bool: ...
+    @overload  # type: ignore
+    def __rxor__(self, x: int) -> int: ...
 
 class slice:
     start = ...  # type: Optional[int]