The dual of a Boolean function $$F\left( {{x_1},{x_2},\,....,\,{x_n},\, + , \cdot ,'} \right),$$ written as $${F^D}$$, is the same expression as that of $$F$$ with $$+$$ and $$ \cdot $$ swapped. $$F$$ is said to be self-dual if $$F = {F^D} \cdot $$. The number of self-dual functions with $$n$$ Boolean variables is

Which one of the following expressions does NOT represent exclusive NOR of $$x$$ and $$y?$$

The simplified $$SOP$$ (Sum of product) form of the Boolean expression
$$\left( {P + \overline Q + \overline R } \right).\left( {P + \overline Q + R} \right).\left( {P + Q + \overline R } \right)$$ is

Which one of the following circuits is NOT equivalent to a $$2$$-input $$XNOR$$ (exclusive NOR) gate