You can use Compare-Object to compare the value pairs as arrays:
if (Compare-Object $a, $b $c, $d -SyncWindow 0) {
'different'
} else {
'same'
}
Note that this is convenient, but relatively slow, which may matter in a loop with many iterations.
The Compare-Object cmdlet compares two arrays and by default returns information about their differences.
-SyncWindow 0 compares only directly corresponding array elements; in other words: $a must equal $c, and $b must equal $d; without -SyncWindow, the array elements would be compared in any order so that 1, 2 would be considered equal to 2, 1 for instance.
Using the Compare-Object call's result as a conditional implicitly coerces the result to a Boolean, and any nonempty result - indicating the presence of at least 1 difference - will evaluate to $True.
As for what you tried:
Use of { ... } in your conditional is not appropriate.
Expressions enclosed in { ... } are script blocks - pieces of code you can execute later, such as with & or .
Even if you used (...) instead to clarify operator precedence (-ne has higher precedence than
-and), your conditional wouldn't work as expected, however:
($a -and $b) -ne ($c -and $d) treats all variables as Booleans; in effect, given PowerShell's implicit to-Boolean conversion, you're comparing whether one value pair has at least one empty string to whether the other doesn't.