Answer
$\left[ {\begin{array}{*{20}{c}}
1&0\\
1&1\\
1&1
\end{array}} \right]$
Work Step by Step
$\begin{array}{l}
A \odot B = \left[ {\begin{array}{*{20}{c}}
1&0&0&1\\
0&1&0&1\\
1&1&1&1
\end{array}} \right] \odot \left[ {\begin{array}{*{20}{c}}
1&0\\
0&1\\
1&1\\
1&0
\end{array}} \right]\\
= \left[ {\begin{array}{*{20}{c}}
{(1 \wedge 1) \vee (0 \wedge 0) \vee (0 \wedge 1) \vee (1 \wedge 1)}&{(1 \wedge 0) \vee (0 \wedge 1) \vee (0 \wedge 1) \vee (1 \wedge 0)}\\
{(0 \wedge 1) \vee (1 \wedge 0) \vee (0 \wedge 1) \vee (1 \wedge 1)}&{(0 \wedge 0) \vee (1 \wedge 1) \vee (0 \wedge 1) \vee (1 \wedge 0)}\\
{(1 \wedge 1) \vee (1 \wedge 0) \vee (1 \wedge 1) \vee (1 \wedge 1)}&{(1 \wedge 0) \vee (1 \wedge 1) \vee (1 \wedge 1) \vee (1 \wedge 0)}
\end{array}} \right]\\
= \left[ {\begin{array}{*{20}{c}}
{1 \vee 0 \vee 0 \vee 1}&{0 \vee 0 \vee 0 \vee 0}\\
{1 \vee 1 \vee 1 \vee 1}&{0 \vee 1 \vee 0 \vee 0}\\
{1 \vee 0 \vee 1 \vee 1}&{0 \vee 1 \vee 1 \vee 0}
\end{array}} \right]\\
= \left[ {\begin{array}{*{20}{c}}
1&0\\
1&1\\
1&1
\end{array}} \right]
\end{array}$
