Final answer:
A diverging lens always forms a virtual and upright image, while a converging lens does not always produce a real and inverted image, as it can form virtual images too. The image formed by a diverging lens is always closer to the lens, and statement about a real image formed by a converging lens being always smaller is incorrect.
Step-by-step explanation:
Regarding the image formation by lenses, we can determine the following based on the provided exploration data:
(i) A diverging lens always forms a virtual and upright image, which is true as diverging lenses can only produce case 3 images that are always virtual, upright, and smaller than the object.
(ii) A converging lens always forms an image that is real and inverted is not entirely true as it can also form virtual images when the object is within the focal length of the lens (case 2).
(iii) The image formed by a diverging lens is always closer to the lens than the object, which is true, as indicated in the case 3 image formation.
(iv) The statement that the image formed by a converging lens is always farther away from the lens than the object is incorrect because this is only the case when the image is virtual and the object is closer than the lens's focal length (case 2).
(v) A real image formed by a converging lens is always smaller than the object is not always true as real images can be either larger or smaller than the object, depending on the object's distance from the lens relative to the focal length.