Question

Let R={(1,1),(1,2).(2.1).(2.2)} be a relation on A={1,2).The transitive closure of R is

Answer 1

We need to recall the following definition of transitive closure.

• $R$ be a relation on a set $A$ with $n$ elements. Then the transitive closure of $R$ is $R^*=R\cup R^2\cup .....\cup R^n$.

Given:

$R=\{(1,1),(1,2),(2,1),(2,2)\}$ is a relation on $A=\{1,2\}$

From the definition of transitive closure, we get

The transitive closure of $R$ is, $R^*=R\cup R^2$ .

We get,

$R^2=R\circ R={\(1,1),(1,2),(2,1),(2,2)\}$

Hence, the transitive closure is,

$R^*=\{(1,1),(1,2),(2,1),(2,2)\}$