Bloom filter gives a \(O(1)\)-efficient way to test for set memberships, but with false positives and no false negatives, i.e. it will tell you \(x\in S\) while actually it is not, but not vice versa.
To get a data structure for similar set membership testing, but with false negatives only, is an interesting problem. Google it you will see the (only?) solution as a direct-mapped cache. Use a fix-size hash table and a hash function, and assume the item is hashable and comparable, then
class cache: size = 100 table = [None]*size def add(item): table[hash(item) % size] = item def isMember(item): return table[hash(item) % size] == item
It has false negative because the item in the hash table could be erased.