Consider the function defined over three binary variables:

$f(x_1,x_2,x_3)=(not{x}_1^{{?}^{?}}not{x}_2^{{?}^{?}}not{x}_3).$

We aim to find a $$ such that, for any $x=[x_1,x_2,x_3],$ where $x_{i}in\{0,1\}$ :

$*x+{}_0>0$ when $f(x_1,x_2,x_3)=1,$ and

$*x+{}_0<mn\; id="EditorElement\_1547493">0</mn>$ when $f(x_1,x_2,x_3)=0.$

If ${}_0=0($no offset$),$ would it be possible to learn such a $?$

Yes

No

Would it be possible to learn the pair $$ and ${}_0?$

No