Question

Let R be the relation {(1,1),(1,3),(2,2),(3,1),(3,2)}.

(a) Find the 3x3 matrix MR representing R.

(b) Find the matrix representing the transitive closure of R.

Answer 1

(a) $\begin{bmatrix} 1 & 0 & 1 \\ 0 & 1& 0 \\ 1 & 1& 0 \end{bmatrix}$

(b)  transitive closure of R {(1,1),(1,3),(2,2),(3,1),(3,2),(1,2),(3,3)}

$\begin{bmatrix} 1 & 1 & 1 \\ 0 & 1& 0 \\ 1 & 1& 1 \end{bmatrix}$