$$f\left( {A,B} \right) = A' + B$$ Simplified expression for function $$f((x+y,y),z)$$ is

Transform the following logic circuit (without expressing its switching function) into an equivalent logic circuit that employs only $$6$$ $$NAND$$ gates each with $$2$$-inputs.

Consider the following logic circuit whose inputs are functions $${f_1},$$ $${f_2},$$ $${f_3},$$ and output is $$f.$$

The simultaneous equations on the Boolean variables $$x, y, z$$ and $$w,$$ $$$x+y+z=1$$$ $$$xy=0$$$ $$$xz+w=1$$$ $$$xy + \overline z \overline w = 0$$$
have the following for $$x, y, z$$ and $$w,$$ respectively.