Consider a simple neural network with the below architecture. Assume the network uses a step activation function $($with a threshold or $0).$ Recall that you can think of a network like this as a function that accepts two inputs, $x_2$ and $,$ and produces a single output $|y.$

For each of the following functions, state what values of $w0,v2,$ and $\sqrt[\phantom{2}]{2}$ would result in this network implementing that function. If no choice of weights is possible, explain why.

The AND function, which takes two binary $|$l or $1)$ inputs and outputs a $1$ if and only if both inputs arc $1.$

The NAND function, which outputs the opposite of whatever AND outputs.

The XOR function, which outputs $1$ If and only if exacty one of its inputs is $1.$