Explanation:

To find the number of non-empty even subsets of a set with n elements, we can consider the following approach:

1. Understanding the Problem:
Let's assume the set has n elements. We want to count the number of non-empty even subsets, i.e., subsets that have an even number of elements.

2. Counting the Subsets:
To count the subsets, we need to consider each element independently. For each element in the set, we have two choices: include it in the subset or exclude it from the subset. Therefore, for n elements, we have a total of 2^n subsets.

3. Excluding the Empty Subset:
The problem asks for non-empty even subsets, so we need to exclude the empty subset from our count. Since the empty subset has no elements, we subtract 1 from the total number of subsets.

4. Counting the Even Subsets:
To count the even subsets, we need to consider the parity of the number of elements in each subset. For an even subset, we can choose 0, 2, 4, 6, ..., or n elements from the set. This means we have (n choose 0) + (n choose 2) + (n choose 4) + ... + (n choose n) even subsets.

5. Using the Binomial Theorem:
The sum (n choose 0) + (n choose 2) + (n choose 4) + ... + (n choose n) can be simplified using the binomial theorem. The binomial theorem states that for any positive integer n:

(n choose 0) + (n choose 1) + (n choose 2) + ... + (n choose n) = 2^n

Since we are only interested in the even subsets, we can divide this sum by 2 to obtain the number of even subsets:

Number of even subsets = (1/2) * (2^n)

6. Final Answer:
Substituting the value of the total number of subsets (2^n - 1) from step 3, we get:

Number of even subsets = (1/2) * (2^n - 1) = 2^(n-1) - 1

Therefore, the correct answer is option C: 2^(n-1) - 1.