Assuming $arr is the array, you can do like this:
$computers = $arr | select -expand computer -unique
$arr | group uid | ?{$_.count -eq $computers.count} | select name
In general, I would approach union and intersection in Powershell like this:
$a = (1,2,3,4)
$b = (1,3,4,5)
$a + $b | select -uniq #union
$a | ?{$b -contains $_} #intersection
But for what you are asking, the above solution works well and not really about union and intersection in the standard definition of the terms.
Update:
I have written pslinq which provides Union-List and Intersect-List that help to achieve set union and intersection with Powershell.