The minters expansion of $$f\left( {P,Q,R} \right) = PQ + Q\overline R + P\overline R $$ is

What is the minimum number of gates required to implement the Boolean function $$(AB+C)$$ if we have to use only $$2$$-input NOR gates?

Given $${f_1},$$ $${f_3},$$ and $$f$$ in canonical sum of products form (in decimal) for the circuit. $$${f_1} = \sum {m\left( {4,5,6,7,8} \right)} $$$ $$${f_3} = \sum {m\left( {1,6,15} \right)} $$$ $$$f = \sum {m\left( {1,6,8,15} \right)} $$$
Then $${f_2}$$ is

Consider the following Boolean function with four variables
$$F\left( {w,\,x,\,y,\,z} \right) = \sum {\left( {1,\,3,\,4,\,6,\,9,\,11,\,12,\,14} \right)} $$ the function is