Logical operators $($i$.$e$.$ NOT, AND, OR$,$ XOR, etc$)$ are the building blocks of any computational device.

Logical functions return only two possible values, true or false, based on the truth or false values of

their arguments. For example, operator AND returns true only when all its arguments are true,

otherwise $($if any of the arguments is false$)$ it returns false. If we denote truth by $1$ and false by $0,$ then

logical function AND can be represented by the following table:

This function can be implemented by a single$-$unit with two inputs:

if the weights are $w1=1$ and $w2=1$ and the activation function is:

$(v)=\{\begin{array}{ccc}1& if& v2\\ 0& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}$

Note that the threshold level is $2(v2).$

a$)$ Test how the neural AND function works.

b$)$ Suggest how to change either the weights or the threshold level of this single$-$unit in order to

implement the logical OR function $($true when at least one of the arguments is true$)$:

c$)$ The XOR function $($exclusive or$)$ returns true only when one of the arguments is true and another

is false. Otherwise, it returns always false. This can be represented by the following table:

Do you think it is possible to implement this function using a single unit? A network of several units?