Dynamic Bloom filters (DBF) were proposed by Guo et. al. in 2010 to tackle the situation where the size of the set to be stored compactly is not known in advance or can change during the course of the application. We propose a novel competitor to DBF with the following important property that DBF is not able to achieve: our structure is able to maintain a bound on the false positive rate for the set membership query across all possible sizes of sets that are stored in it. The new data structure we propose is a dynamic structure that we call Dynamic Partition Bloom filter (DPBF). DPBF is based on our novel concept of a Bloom partition tree which is a tree structure with standard Bloom filters at the leaves. DPBF is superior to standard Bloom filters because it can efficiently handle a large number of unions and intersections of sets of different sizes while controlling the false positive rate. This makes DPBF the first structure to do so to the best of our knowledge. We provide theoretical bounds comparing the false positive probability of DPBF to DBF.