Final answer:
The equivalent method definition to the given one is option (c). It correctly compares each element in an ArrayList with the specified object and increments a counter when matches are found.
Step-by-step explanation:
The correct method definition that is equivalent to the given one is option (c). This method counts how many times an object appears in an ArrayList. Both the original method and option (c) use a loop to traverse the list and use the .equals method to compare each element in the list with the given thing. Whenever they match, the count variable is incremented. Option (b) incorrectly increments the count for every element in the list, regardless of whether or not it matches thing. Option (d) increments the count when the elements do not match thing, which is the opposite of what we want. Finally, option (e) will give a count of all items in the list because list.contains(item) will always return true as it checks whether the list contains the item currently being iterated over, which it does.
The method definition that is equivalent to the given one and returns the same value in every possible case is option b.
In option b, the method iterates through the list using a for-each loop and increments the count for each item in the list. The loop iterates through the list and does not make any comparisons, thus ensuring that the count is always the same as the size of the list.
For example, if we have a list with 5 elements and we pass it to option b's method, the count will always be 5 because the loop will iterate through all 5 elements without any conditions.