Answered! Find transitive closure using matrices and Algorithm 1: {1,2,3,4} A) {(1, 2), (2, 1), (2, 3), (3, 4) (4, 1)}…

Find transitive closure using matrices and Algorithm 1: {1,2,3,4}

A) {(1, 2), (2, 1), (2, 3), (3, 4) (4, 1)}

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Expert Answer

We can use Warshall’s algorithm for finding the Transitive Closure of a matrix. By using the formula below we can construct The Relation matrix $R^{1}$ from $R^{0}$ .

$R^{1}[i,j]=R^{0}[i,j] OR (R^{0}[i,k] and R^{0}[k,j])$

where $R^{0}$ is the adjacency matrix of given data. k is the relation degree.

For Given data the adjacency matrix $R^{0}$ is given below.

By using the formula mentioned above, Consider the first row and first column, The matrix $R^{1}$ will be:

So $R^{4}$ will be the transitive closure of the given data.

Hence the solution provided.

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