BUG: When done as part of pd.Series, `NaN | True` is `False` which contradicts logic

[corneliusroemer]

Pandas version checks

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Reproducible Example

import pandas as pd
df = pd.DataFrame([{"a": True}, {"b":True}])
df["a"]|df["b"]

Issue Description

The result of a bitwise or operator (| or pd.Series.__or__()) should not depend on the order of the operands. Or should be commutative.

But in this case, when one of the operands is NaN, pandas violates this law. This seems odd. Numpy doesn't show this inconsistency. Numpy complains that NaN cannot be used with Or.

Pandas silently casts, without any warning.

There's been a StackOverflow issue about this for a long time, but I couldn't find an issue here: https://stackoverflow.com/questions/39000907/pandas-column-selection-non-commutative-bitwise-or-when-selecting-on-str-and-na

Expected Behavior

The result should always be true in bitwise or comparison if one of the operands is true.

It's ok if the user gets a warning or there's an error. But silently making it go false is bad.

Actual behavior

> df
	a	b
0	True	NaN
1	NaN	True
> df["a"]|df["b"]
0    True
1     False
dtype: bool

Installed Versions

INSTALLED VERSIONS

commit : 2e218d1
python : 3.10.8.final.0
python-bits : 64
OS : Darwin
OS-release : 22.3.0
Version : Darwin Kernel Version 22.3.0: Thu Jan 5 20:48:54 PST 2023; root:xnu-8792.81.2~2/RELEASE_ARM64_T6000
machine : x86_64
processor : i386
byteorder : little
LC_ALL : None
LANG : en_GB.UTF-8
LOCALE : en_GB.UTF-8

pandas : 1.5.3
numpy : 1.24.2
pytz : 2022.7.1
dateutil : 2.8.2
setuptools : 67.1.0
pip : 23.0
Cython : None
pytest : 7.2.1
hypothesis : None
...
xlrd : None
xlwt : None
zstandard : 0.19.0
tzdata : None

[corneliusroemer]

Possible duplicate of #41604

[topper-123]

This is a bit of edge case for pandas as generally (outside of pandas) we have that

>>> True | 1.5
TypeError: unsupported operand type(s) for |: 'bool' and 'float'
>>> True | np.nan
TypeError: unsupported operand type(s) for |: 'bool' and 'float'
>>> True | None
TypeError: unsupported operand type(s) for |: 'bool' and 'NoneType'

So in this case you are working with object dtypes with incompatible data, which is never fun.

We do have some half-baked support for this, but I'd strongly recommend convert to "boolean" dtype when working with booleans with nan data.

So IDK, it's probably almost hopeless to support all "expected" cases when using object dtypes. I guess you could try to see if you can patch this to work, but I think it has to be relatively simple to be accepted.