Get-WmiObject using AND or OR (they are working in the opposite manner) - filtering

Question

It seems like WMI filtering using multiple criteria (AND and OR) is not working properly. In fact, the AND behaves like OR should, and the OR behaves like the AND should. Maybe it's just me, but I am wondering if anyone else is seeing this behavior.
I am trying to get a list of Windows shares using PowerShell and Get-WMIObject, which works great: Get-WmiObject -Class Win32_Share
My brain has exploded because using either a WQL statement or a WMI filter, for me, results in the AND and OR operators behaving in the exact opposite manner they should.
Take these shares as an example: Admin$, C$, D$, TestShare
If I wanted to exclude C$ and D$ from my results, I could filter it using a WQL statement
("SELECT * from Win32_Share WHERE Name !='C$' OR Name !='D$'") or a WMI filter (-Filter "Name <>'C$' OR Name <> 'D$'")
Unfortunately, when running either option, say this one:
Get-WmiObject -Class Win32_Share -Filter "Name <>'C$' OR Name <> 'D$'"
PowerShell returns a list of all four shares, Admin$, C$, D$, and TestShare. It is as if PowerShell is treating the OR as an AND, and therefore the criteria doesn't match, so all results are returned.
The crazy thing is, if I replace the OR with an AND, I get the results I want. Running this:
Get-WmiObject -Class Win32_Share -Filter "Name <>'C$' AND Name <> 'D$'"
gives me a list of shares: Admin$ and TestShare, excluding C$ and D$. This seems like PowerShell is treating the AND as an OR. I tested this in PowerShell 2, 3, and 5; same result in each.
Looking online for WMI filtering using OR examples, they are all exactly as one would expect, so why the heck am I seeing this backwards behavior?
Can anyone else re-create my issue, or figure out why I am seeing this in my environment? Thanks

Answer 1

Go back to propositional logic and boolean algebra basics. In particular, De Morgan's laws can be expressed in English as:
the negation of a disjunction is the conjunction of the negations; and
the negation of a conjunction is the disjunction of the negations.
Take these shares as an example: print$, IPC$, Test, TestC:
PS D:\PShell> Get-WmiObject -Class Win32_Share
Name Path Description
---- ---- -----------
IPC$ Remote IPC
print$ C:\Windows\system32\spool\drivers Ovladače tiskárny
test D:\test
testC C:\testC
To excerpt only print$ and IPC$, then your filter should be "Name='IPC$' or Name='print$'":
PS D:\PShell> Get-WmiObject -Class Win32_Share -Filter "Name='IPC$' or Name='print$'"
Name Path Description
---- ---- -----------
IPC$ Remote IPC
print$ C:\Windows\system32\spool\drivers Ovladače tiskárny
Vice versa, let's exclude both print$ and IPC$ from the result i.e. take the filter negation:
PS D:\PShell> Get-WmiObject -Class Win32_Share -Filter "not (Name='IPC$' or Name='print$')"
Name Path Description
---- ---- -----------
test D:\test
testC C:\testC
The latter result is the same for the following filters (apply propositional logic rules successively):
"not (Name = 'IPC$' or Name = 'print$')": above original
"not (Name = 'IPC$') AND not (Name = 'print$')": De Morgan Laws applied
" Name <> 'IPC$' AND Name <> 'print$'"  : comparison operators negated