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$R$ and $S$ are two relations on a set $A$

\begin{align*} M_R = \begin{bmatrix} 1 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ \end{bmatrix} \qquad M_S = \begin{bmatrix} 0 & 1 & 1 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \\ \end{bmatrix} \end{align*}

Then matrices for $R \cap S$ and $R \cup S$ ?
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And & Or respectively.
separately
Yes. For union, OR each correspond element . For intersection, AND.

Union of matrix is boolean OR and intersection of matrix is boolean AND.

$M_{R} \cup M_{S}= \begin{bmatrix} 1 &1 &1 \\ 1 & 1& 0\\ 1 & 1 & 0 \end{bmatrix} M_{R}\cap M_{S}=\begin{bmatrix} 0&0 & 1\\ 0 & 0 &0 \\ 0 &1 &0 \end{bmatrix}$