Final answer:
The false statement is that diamonds are found in pegmatites; diamonds form in kimberlite, not pegmatites. Pegmatites are igneous rocks that contain large crystals and are not associated with diamonds.
Step-by-step explanation:
The statement that is FALSE among the options provided regarding diamonds is "Diamonds are found in carrot-shaped structures called pegmatites." Diamonds are indeed brought up from the mantle to the surface in magma that hardens into kimberlite, and they can end up in stream gravels after weathering out of ore bodies. Industrial quality diamonds are used as abrasives due to their hardness. However, diamonds are not typically found in pegmatites, which are instead igneous rocks known for containing large crystals and forming in the final stages of magma cooling, but not usually associated with diamond formation.