(Solved): 1. (50 pts) Design a two-layer neural network with the signum activation function (i.e. \( \operat ...

1. (50 pts) Design a two-layer neural network with the signum activation function (i.e. \( \operatorname{sgn}(x)=1 \) if \( x>0, \operatorname{sgn}(x)=-1 \) if \( x<0 \), and \( \operatorname{sgn}(0)=0) \) such that the network implements the logic gate \( f\left(x_{1}, x_{2}, x_{3}\right)=\overline{x_{1}} x_{2} x_{3}+x_{1} \overline{x_{2}} \). Assume that the input of \( -1 \) is used to represent a FALSE, and an input of 1 is used to represent a TRUE. Show your work and draw the final network. Note that in class, we have discussed examples where we have instead used the step activation function and a 0 for FALSE.