Which are the essential prime implicants of the following Boolean function? $$F\left( {a,b,c} \right) = {a^1}c + a{c^1} + {b^1}c$$

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

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

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.