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Problem A$.2$

While simple Boolean functions can be realized notionally with a single McCulloch$-$Pitts $($MP$)$ neuron, computation of more involved Boolean functions such as$,$ XOR, AND$-$NOT $($NAND$)$ etc. needs an interconnected set of more than a single neuron with an output decision logic decided by a threshold:

Example: AND operation via single MP neuron

Truth table for AND operation

Output decision

$y=1$ if $y$ Threshold, $$

$=0$ if $y$ Threshold, $$

Suppose:

$x_1=1$ and $x_2=1$

$y=2$

Let: $=0$

Therefore,

Output decision: Logic $1$

Truth Table

$\backslash$table$[[P,Q,P$&$Q$