Answer to Question #238829 in Discrete Mathematics for Harsha

Question

find the transitive closure of (1 3) (5 5) (1 6) (3 3) (5 6)

Answer 1

Solution:

The transitive closure of a binary relation R on a set A  is the smallest transitive relation t(R)

 on A containing R.

Given, R = {(1 3), (5 5), (1 6), (3 3), (5 6)}.

If we add (3,6) to R, then $(1,3),(3,6)\in R \Rightarrow(1,6)\in R$ .

Thus, transitive closure is {(1 3), (3,6), (5 5), (1 6), (3 3), (5 6)}