Question

transitive closure of{(1,3),(5,5),(1,6),(3,3),(5,6)}

Answer 1

The transitive closure of the relation $R=\{(1,3),(5,5),(1,6),(3,3),(5,6)\}$ is the smallest transitive relation that contains $R.$ Since for relation $R$ we have that $(a,b)\in R$ and $(b,c)\in R$ imply $(a,c)\in R$ for all pairs that belong to $R,$ we conclude that $R$ is transitive, and hence its transitive closure is equal to $R.$