Chapter 8, Problem 51RE

(a)

To determine

The number of subsets of a set with n elements of size 0, of size 1, of size 2, of size n.

(b)

To determine

The total number of subsets of a set with n elements.

(c)

To determine

The reason why the equation $C\left(n,0\right)+C\left(n,1\right)+C\left(n,2\right)+\cdots +C\left(n,n\right)=2^n$ is true.

(d)

To determine

To verify: The equation $C\left(n,0\right)+C\left(n,1\right)+C\left(n,2\right)+\cdots +C\left(n,n\right)=2^n$ for $n=4$ and $n=5$.

(e)

To determine

To write: The relation of the equation $C\left(n,0\right)+C\left(n,1\right)+C\left(n,2\right)+\cdots +C\left(n,n\right)=2^n$ with Pascal’s triangle.