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## Homework Statement

Let N={1,2...n} .Define the Power set of N,P(N).

a) show that the map f:P(N)->P(N)

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

b)C(n,k)=C(n,n-k).

## The Attempt at a Solution

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 . The domain and range have the same cardinality since we are using the power set of N.and f:N->N is bijective maybe a logical consequence will be that f:P(N)->P(N) is also bijective

Also |N\A|=n-|A| where | | represents the number of elements in a set.

Ineed help in solving a ) and b)