Vegetative propagation is a type of asexual reproduction in plants in which a new plant grows from a vegetative part of the parent plant—that is, from a root, stem or leaf—instead of from seeds. Because no gametes are involved, the offspring is genetically identical to the parent.

Statement A is correct: under suitable conditions of moisture, warmth and nutrients, the roots, stems and leaves of many plants can give rise to whole new plants (for example, the buds ("eyes") on a potato stem tuber, or the leaf margins of Bryophyllum which sprout new plantlets).

Statement B is also correct: vegetative propagation is widely used in agriculture and horticulture—sugarcane is grown from stem cuttings, roses are propagated by cuttings/grafting, and grapes are commonly raised from stem cuttings and layering. This lets growers quickly produce many identical, desirable plants.

Since both statements are accurate, both A and B are correct.

Hence, the answer is Both Statement A and B.