If you delete someone from your Facebook friends will they know it?

They won't get any notice of it, but if they go through their friends list they won't see you. That might give them a hint...

Yes, it is very possible for your friends to determine if you deleted them from your friend list specially if they have applications that has the ability to track this records such us

Facebook Friend Checker

http://thesocialmediaguide.com/social_media/removed-from-friends-list-facebook

Unfriend Finder

http://darktips.com/find-out-who-deleted-you-in-your-friendlist-on-facebook/

Who Deleted Me

http://www.YouTube.com/watch?v=f5ui9zYvPb4