Question

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

Answer 1

The number of elements in the power set of a set with c elements is 2c.

Step-by-step explanation:

The number of elements in the power set of a set with c elements is 2c. This means that the power set contains all possible subsets of the original set, including the empty set and the set itself.

For example, if c = 3, then the original set has 3 elements. The power set will have 2³= 8 elements. These elements are: {}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}.

Therefore, the number of elements in the power set is 2 to c.

Answer 2

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.