Introduction:
When checking whether a given set of items is sorted, it is important to consider the efficiency of the sorting algorithm used. In this scenario, the set of items is already in sorted order, which means that the algorithm should be able to detect this efficiently without unnecessary comparisons or swaps. Two sorting methods that are efficient for this purpose are Bubble Sort and Insertion Sort.

Bubble Sort:
Bubble Sort is a simple comparison-based sorting algorithm. It works by repeatedly swapping adjacent elements if they are in the wrong order until the entire set is sorted. In the case of a sorted set, Bubble Sort can efficiently detect this as it will only require a single pass through the set without any swaps. This makes Bubble Sort a suitable choice for checking whether a set is sorted.

Insertion Sort:
Insertion Sort is another comparison-based sorting algorithm that works by dividing the set into sorted and unsorted portions. It iterates through the unsorted portion, comparing each element with the elements in the sorted portion, and inserting it at the correct position. In the case of a sorted set, Insertion Sort will require minimal comparisons and swaps, making it an efficient choice for checking whether a set is sorted.

Efficiency comparison:
1. Bubble Sort: In the worst-case scenario, where the set is completely unsorted, Bubble Sort has a time complexity of O(n^2). However, in the case of a sorted set, it has a best-case time complexity of O(n), as it only requires a single pass without any swaps.
2. Selection Sort: Selection Sort is not efficient for this scenario because it always requires a complete pass through the set, even if it is already sorted. It has a time complexity of O(n^2) regardless of the order of the set.
3. Insertion Sort: Similar to Bubble Sort, Insertion Sort has a time complexity of O(n) in the best-case scenario when the set is already sorted. It only requires minimal comparisons and swaps to detect the sorted order.
4. Merge Sort: Merge Sort is a divide-and-conquer algorithm that has a time complexity of O(n log n) in all cases. While it guarantees a sorted set, it is not efficient for checking whether a set is already sorted.

Conclusion:
Based on the efficiency analysis, the most efficient sorting methods for checking whether a given set of items is already in sorted order are Bubble Sort and Insertion Sort. Both algorithms have a best-case time complexity of O(n) when the set is already sorted, making them suitable choices for this scenario.