$[$Simple network $(20$ points$)]$ The truth table of XOR is provided as follows.

a$.$ Briefly argue $($no need to put up a formal proof$)$ that no Logistic Regression model can perfectly

classify this dataset.

b$.$ XOR can be reformulated as XOR OR $\{$:$x_2)$ AND $($NOT AND $\{$:$x_2)).$ You are asked,

based on this formulation, to construct a neural network for XOR. The network should have $2$

input units, $1$ hidden layer with $2$ units using sigmoid as activation function, and $1$ output unit

using sigmoid as output function.

Please draw the network and provide the weights and biases on the edges $($or nodes$).$ Briefly

explain your design.