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