Final Answer:
The set S={a,b,c,d} has 4 one-element subsets.
Step-by-step explanation:
A one-element subset of a set contains exactly one element from the original set. In set S={a,b,c,d}, the possible one-element subsets are {a}, {b}, {c}, and {d}. Each element in the set S can form a distinct one-element subset. The count of one-element subsets is equal to the number of elements in the original set.
Mathematically, the number of one-element subsets (denoted as N) for a set with n elements can be calculated using the formula N = 2^n. In this case, the set S has 4 elements, so N = 2^4 = 16. However, this counts all possible subsets, including the empty set and the set itself. To find the number of distinct one-element subsets, we subtract these two cases: 16 - 2 = 14. Therefore, there are 14 subsets that contain exactly one element.
In summary, the set S={a,b,c,d} has 4 one-element subsets, each corresponding to a distinct element in the set. The calculation involves using the formula N = 2^n, where n is the number of elements in the original set, and adjusting for the exclusion of the empty set and the set itself to find the correct count.