5. according to carnegie’s beliefs, what insures the survival of the fittest in every department and is essential to the future progress of the man?

Although ethically controversial and still a discussed issue today, the answer to this question is the "natural law of competition" born in " the great inequality of environment, the concentration of business—industrial and commercial—in the hands of a few", as Carnegie wrote in his "Gospel of Wealth". 

H. klkl