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The transitive closure of a relation $R$ on set $A$ whose relation matrix $\begin{bmatrix}
0 & 1 & 0\\ 
0 & 0 & 1 \\ 
1 & 0 & 0
\end{bmatrix}$ is :

  1. $\begin{bmatrix}
    0 & 1 & 0\\ 
    0 & 0 & 1 \\ 
    1 & 0 & 0
    \end{bmatrix}$
  2. $\begin{bmatrix}
    1 & 1 & 0\\ 
    1 & 1 & 0 \\ 
    1 & 1 & 0
    \end{bmatrix}$
  3. $\begin{bmatrix}
    1 & 1 & 1\\ 
    1 & 1 & 1 \\ 
    1 & 1 & 1
    \end{bmatrix}$
  4. $\begin{bmatrix}
    0 & 1 & 1\\ 
    0 & 1 & 1 \\ 
    0 & 1 & 1
    \end{bmatrix}$

 

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