To find the probability that a randomly chosen subset S from U does not have two consecutive elements, we can consider the number of subsets that do not have two consecutive elements and divide it by the total number of non-empty subsets.

Total number of non-empty subsets:
The set U has 5 elements, so the total number of subsets (including the empty set) is 2^5 = 32. However, we need to subtract 1 from this total to exclude the empty set, so the total number of non-empty subsets is 32 - 1 = 31.

Number of subsets that do not have two consecutive elements:
To count the number of subsets that do not have two consecutive elements, we can use a recursive approach. Let's define a function f(n) as the number of such subsets for a set of size n.

For n = 1, there is only one subset {1} that does not have two consecutive elements, so f(1) = 1.
For n = 2, there are two subsets {1} and {2} that do not have two consecutive elements, so f(2) = 2.
For n > 2, we can consider two cases:
1. The subset does not include the last element (n). In this case, we can choose any subset that does not have two consecutive elements from the set {1, 2, ..., n-1}, which is equivalent to f(n-1).
2. The subset includes the last element (n). In this case, the second-to-last element (n-1) cannot be included in the subset, so we need to choose any subset that does not have two consecutive elements from the set {1, 2, ..., n-2}, which is equivalent to f(n-2).

Therefore, we can define the recursive formula for f(n) as:
f(n) = f(n-1) + f(n-2)

Using this formula, we can calculate the values of f(n) for n = 1, 2, 3, 4, 5:
f(1) = 1
f(2) = 2
f(3) = f(2) + f(1) = 2 + 1 = 3
f(4) = f(3) + f(2) = 3 + 2 = 5
f(5) = f(4) + f(3) = 5 + 3 = 8

Therefore, the number of subsets that do not have two consecutive elements is f(5) = 8.

Probability calculation:
The probability that S does not have two consecutive elements can be calculated by dividing the number of subsets that do not have two consecutive elements by the total number of non-empty subsets:

Probability = number of subsets that do not have two consecutive elements / total number of non-empty subsets
Probability = 8 / 31

Therefore, the correct answer is option D) 8/31, not option D) 12/31 as stated in the question.