>>12477205
you're statement's incorrect for all sets of some, some being all non empty subsets of U, therefore your statement's the complement of one of the complements of the original statemen, which means that for n=1 with N>=1 your definition's actually the oppsite of the true negation of the expression (when some means all) and in no case it's correct (some is never none)
Your fortune: Excellent Luck