So far, most of association rule minings have considered about positive association rules based on frequent itemsets in databases[2,5-7], but they have not considered the problem of mining negative association rules correlated with frequent and infrequent itemsets. Negative association rule mining is much more difficult than positive association rule mining because it needs infrequent itemsets, and only the rare association rule mining which is a kind of negative association rule minings has been studied. This paper presents a mathematical model to mine positive and negative association rules precisely, for which in a point of view that negation of a frequent itemset is an infrequent itemset, we make clear the importance of the problem of mining negative association rules based on certain infrequent itemsets and study on what conditions infrequent itemsets of interest should satisfy for negative association rules.