Three algorithms, based on a matrix structure, are described here. First of them generates all monotone Boolean functions of n variables in lexicographic order. The second one determines the first (resp. the last) lexicographically minimal true (resp. maximal false) vector of an unknown function. It serves the third algorithm, which identifies an unknown monotone Boolean function f of n variables by using membership queries only. For up to 6 variables it determines f with at most m.n queries, where m is the combined size of the sets of minimal true and maximal false vectors of f.