Question

If c is a set with c elements how many elements are in the power set of c

Answer 1

There would be 2 raised to c elements in the power set. Elements of the power set are formed by making a binary decision on each element of the input set: include or do not include. Since there are two choices for each element of the input set, and there are c elements in the input set, there are 2^c possible arrangements of these input elements.