Question #188660

A={1,2,3,4} and R={(1,2),(3,4),(2,1)}.find transitive closure of R



1
Expert's answer
2021-05-07T11:33:15-0400

Let A={1,2,3,4}A=\{1,2,3,4\} and R={(1,2),(3,4),(2,1)}R=\{(1,2),(3,4),(2,1)\}. Let us find transitive closure of R.R. Since (1,2)R(1,2)\in R and (2,1)R(2,1)\in R, we conclude that (1,1)(1,1) must belong to the transitive closure of R.R. By analogy, (2,1)R(2,1)\in R and (1,2)R(1,2)\in R imply (2,2)(2,2) must belong to the transitive closure of R.R. It is easy to see that the relation {(1,2),(3,4),(2,1),(1,1),(2,2)}\{(1,2),(3,4),(2,1),(1,1),(2,2)\} is transitive, and hence it is the transitive closure of R.R.


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