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For each given union-closed family F of n elements and m sets, we discuss theunion-closed sets conjecture from height number of the UC family, which is anatural parameter from lattice theory. In this paper, we call it height numberof F(n, m), recorded as H(F). we prove that for any given union-closed familyF, union-closed sets conjecture holds if its height number H(F) no more than 3or no less than n-1. Since the height number H(F) is a positive integer whichis bounded between 1 to n. As an attempted approach and framework, if we canprove union-closed sets conjecture holds for all possible value of H(F), thenunion-closed sets conjecture is true.

Union-closed Sets Conjecture Holds for Height No More Than 3 and Height No Less Than N-1