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Similarity score: Intersection(List1,List2) / Union(List1,List2)

Distance = 1 - Similarity Score

In other words, the similarity score is just the percentage overlap between the two lists and the distance is 0 when the two lists are the same. Say I generalize this to n lists and I calculate the distances between lists (a symmetric matrix of distances). My question is, is this distance formula valid? In other words, does it satisfy the triangle inequality? How do I check this?