Let N={1,2.....n} .Define the Power set of N,P(N), and show that the map f:P(N)->P(N)

defined by taking A to belong to P(N) to N\A is a bijection.

Also prove using the above that

(n)=(n)

(k-1) (k)

Now the power set is defined by P(N)=2^n and a bijection is a one-to-one function that is both injective and surjective.But I don't understand the rest.I"ve been looking at it for the past 1 hour.