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.

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

Express the function $$f( x, y, z)= xy'+ yz'$$ with only one complement operation and one or more $$AND/OR$$ operations. Draw the logic circuit implementing the expression obtained, using a single NOT gate and one or more $$AND/OR$$ gates.

Minimum $$SOP$$ for $$f(w, x, y, z)$$ shown in karnaugh $$-$$ map below is