A regular inspection for a pipe network is conducted at six different regions (denoted 1, 2, 3, 4, 5, and 6). An engineer needs to develop a maintenance schedule for the pipes based on the severity of leaking: no leaking, moderate leaking, and serious leaking. The strategy will be to replace the serious leaking pipes, and to repair the moderately leaking pipes, and to do nothing for the pipes that don't leak. Inspection for each region gave the following percentages for the category of leaking: 3 6 Regions 1 2 4 5 No leaking 0.1 0.3 0.2 0.1 0.40.6 Moderately leaking 0.5 0.4 0.0 0.7 0.6 0.2 Serious leaking 0.4 0.3 0.8 0.2 0.0 0.2 Find the similarity matrix relation R using the cosine amplitude method. Calculate "R-cut using a = 0.8 see which regions belong to which partitions. Also, find the closest transitive relation using transitive max-min closure and do the same partitioning to this relation matrix. Based on this partitioning, which region group would you fix the leakages last? Select one: O i. {5} O ii. {4} O iii. {3} O iv. {1,2} O v. {1,2,4,5} O vi. {1,2,4,5,6} O vii. None of the above