Sir, to me "elegant" is equivalent to "mathematical"!

(Even though I am a failed mathematician, it does sting a little that you felt the need to give me a link to De Morgan's laws.)

True, I did treat this more as a little puzzle than a real world answer, but then what do you expect with only allowing the set operations, "union" and "subtraction"? As for that, you only get the union property as a side effect from hash key creation (which (I think) would not give even a squeak of protest if there were two key/value pairs with identical keys and different values, but by construction we avoid this issue).

Although I've never used this behavior, apparently the delete function does return a list of keys values it's deleted, so delete(@A{keys B}) does return the intersection of A and B ... as well as an undef for every key value that was in B and not in A; so you're back to square 1 with ugly undefs in your answer. (Hence I still haven't used this behavior.) BTW, it just occurred to me that for the symmetric differences %sd1 and %sd2 don't have to be copies of the union, they only need to be the hash equivalents of @array1 and @array2, respectively.

I love talking like a pedant, but in addition to this vice, I have to admit to a hypocrisy: I love using map and grep more, even to the point of using them for their side effects, which means a significant portion of my time in writing up my (few) posts on perlmonks is translating to while and for constructs. So I'm sincere when I say that your original post was elegant enough for me: Handling undefs in perl is just a fact of life, and if you can do it with just one swipe of the knife, then you are about as good as you're going to get without reformulating your approach.

My last gratuitous squeak of protest is that print statements suffice if they work correctly for a code that is an illustration of a solution; in other words, it is not a data structure at that point so much as a formatted solution! (That being said, you've shamed me enough that I will try to start using Data::Dumper in my posts.)

I've just gone through and removed all the smiley's from this post. So now I look smarter, but more crotchety. Anyone who reads this please note that I enjoy these kinds of "pure perl" puzzles and have enjoyed everyone's contribution to this query of LanX's. I spent years as a coder looking for good coders to critique my work with only modest success. Here at perlmonks you get high quality feedback quickly--and you still learn from the low quality feedback because you now have context in which to evaluate it. Good stuff, and thank you LanX.