Solution to Represent each of these relations on {1, 2, 3} with a matrix (with the elements … - Sikademy
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Archangel Macsika

Represent each of these relations on {1, 2, 3} with a matrix (with the elements of this set listed in increasing order). a) {(1, 1), (1, 2), (1, 3)} b) {(1, 2), (2, 1), (2, 2), (3, 3)} c) {(1, 1), (1, 2), (1, 3), (2, 2), (2, 3), (3, 3)} d) {(1, 3), (3, 1)}

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Let us represent each of these relations on \{1, 2, 3\} with a matrix (with the elements of this set listed in increasing order).


a) For the relation \{(1, 1), (1, 2), (1, 3)\} the matrix is the following:


\begin{pmatrix} 1 & 1& 1\\ 0 & 0 & 0\\ 0 & 0 & 0 \end{pmatrix}


b) \{(1, 2), (2, 1), (2, 2), (3, 3)\}


\begin{pmatrix} 0 & 1 & 0\\ 1 & 1 & 0\\ 0 & 0 & 1 \end{pmatrix}


c) \{(1, 1), (1, 2), (1, 3), (2, 2), (2, 3), (3, 3)\}


\begin{pmatrix} 1 & 1& 1\\ 0 & 1 & 1\\ 0 & 0 & 1 \end{pmatrix}


d) \{(1, 3), (3, 1)\}


\begin{pmatrix} 0 & 0 & 1\\ 0 & 0 & 0\\ 1 & 0 & 0 \end{pmatrix}


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