Computer transitive closure of the relation

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1. Compute the transitive closure of the relation below. Show the matrix after each pass of the outermost for loop.2. Show the equivalence classes defined by the transitive closure matrix computed in the previous problem.Assume that rows and columns represent the members of the set {A, B, C, D, E}3. Construct an example of a weighted digraph on which Floyd’s all-pairs shortest paths algorithm would not work correctly if k were varied in the innermost loop instead of the outermost.4. Compute the distance matrix for the digraph whose adjacency matrix is:

1. Compute the transitive closure of the relation below. Show the matrix after each pass of the outermost for loop. [ 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1] 2. Show the equivalence classes defined by the transitive closure matrix computed in the previous problem. Assume that rows and columns represent the members of the set {A, B, C, D, E} 3. Construct an example of a weighted digraph on which Floyd’s all-pairs shortest paths algorithm would not work correctly if k were varied in the innermost loop instead of the outermost. 4. Compute the distance matrix for the digraph whose adjacency matrix is: [ 0 2 4 3 3 0  3 5  0 −3  −1 4 0 ]

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