The association rule is one of the most popular technologies to find the associations between items in large databases. In this paper, we present two efficient algorithms for mining association rules and quantitative association rules, respectively. One is to mine association rules with the Boolean computation according to the Apriori algorithm. The other is to mine association rules including the quantities of items with the Boolean computation by modifying the MQA-1 algorithm proposed by Chen et al. in bag databases. The experiments show that the performances of both algorithms are faster than the algorithm proposed by Wur and Leu's algorithm and the MQA-1 algorithm, respectively.