Question

if R={(1,2),(2,1),(3,1),(2,3)} be a relation defined on A={1,2,3)then transitive closure of R is

Answer 1

The transitive closure is the relation that shows which nodes are reachable from a given node. Since the path 1→2→3→1

1→2→3→1 exists it follows that any node can reach any other node and so $R=A^2$