Note: Use the following perceptron model:

$h(x)=$sign$(w^{T}x)$

where $h(x)$ is the output hypothesis $($which can be $+1$ or $-1),w={\left[\begin{array}{ccc}{w}_0& w_1& w_2\end{array}\right]}^T$ denotes the

weights, and $x={\left[\begin{array}{ccc}1& x_1& x_2\end{array}\right]}^T$ denotes the input vector.

Hint: Describe the target region as a combination of perceptrons which implement linear decision

boundaries. Combine the perceptrons using Boolean operations. Boolean AND and OR operations

$($for two inputs$)$ can be implemented by the perceptron as follows, where $z_1$ and $z_2$ can take the

values $+1$ or $-1.$

$OR(z_1,z_2)=$sign$(z_1+z_2+1\mathrm{.}5)$

AND$(z_1,z_2)=$sign$(z_1+z_2-1\mathrm{.}5)$