First one would check all subsets of n-1 attributes, where there are n attributes total. Then one would check the subsets of n-2 attributes contained in any subset of n-1 attributes which still determined all attributes. If each attribute were a key, then every subset except the whole set and the empty set would be checked. With seven attributes there are 2**7 — 2 = 126 subsets to check. This can be tedious. If there are fifty attributes, there are 2**50 - 2 = 1,125,900,000,000,000 subsets to check (approximately).
An Introduction to Data Base Design by Betty Joan Salzberg (Auth.)