The correct categorization for each assertion is as follows:
I. Language is what distinguishes man from other living beings and allows him not only to interact with the environment, but, above all, dominate it. - True (V)
II. Language enables cultural learning and internalization of cultural products, transmitted from generation to generation. - True (V)
III. Culture, society, and cognition are on the basis of all our ability to think and to say the world. - True (V)
IV. Language is homogeneous, social, cognitive, indeterminate, and invariable. In addition, it can be considered interactive and situated. - False (F)
Therefore, the correct categorization for each assertion is: a. V, V, V, F.