Let the relation R 0 0 0 3 1 0 1 2 2 0 3 2 Find R the trans

Let the relation R = {(0, 0), (0, 3), (1, 0), (1, 2), (2, 0), (3, 2)} Find R\' the transitive closure of R. Show all steps.

Solution

The minimum number of elements needed to be added to the set, so that the overall Relation is transitive

(1,2) belongs to the set, (2,0) belongs to set, so (1,0) must also belong to set which is present

Now (0,3) belongs to the set, (3,2) belongs to the set, so we need to add (0,2) to the set -> First entry

Now (3,2) belongs to the set, (2,0) belongs to the set hence (3,0) will also belongs to the set -> Second entry

Hence the minimum number of entries required are 2

R\' = R U (0,2) U (3,0)

=> { (0,0), (0,3), (0,2), (3,0), (1,0), (1,2), (2,0), (3,2)}