This paper discusses the relationship between algebraic operations on Bloom filters and algebraic operations on data sets.This paper completely define algebraic operations including OR
AND
XOR
NOT
MINUS on Bloom filter
and study the membership query performance on Bloom filter and data set.Theoretical analyses and simulation results show that the Bloom filter ORed (ANDed) from the original Bloom filters can support element membership query on data set ORed (ANDed) from the original data sets