Consider the Boolean function f$2($x$1,$ x$2),$ shown in Table $3.$

instance x$1$ x$2$ f$2($x$1,$ x$2)$

i$1000$

i$2011$

i$3111$

i$4101$

Table $3$: Boolean function f$2($x$1,$ x$2).$

$($a$)$ Draw a diagram to illustrate the hyperplane of a Perceptron neural network

that will correctly classify f$2($x$1,$ x$2).$ Show the cutoff points on the axes. $(5)$

$($b$)$ Calculate the weight values for a neural network that will correctly classify

f$2($x$1,$ x$2).$ Use the threshold function as the activation function $($see Appendix

on p$.6).$ Show all your definitions, steps, and calculations