Step 1: Objective Identification: The task is to associate sociological terms concerning family structures with their precise definitions. The fundamental requirement is to differentiate between rules governing residence, authority, inheritance, and family composition.
Step 2: Definitive Explanations:
(A) Matrilocal Family: "Local" signifies residence. In a matrilocal system, a married couple lives with or near the wife's family. This is determined by the residence rule. (A) corresponds to (II).
(B) Patriarchal Family: "Archal" denotes authority or rule. In a patriarchal family, males, typically the eldest, hold authority and dominance. This indicates male exercise of authority and dominance. (B) corresponds to (III).
(C) Patrilineal Family: "Lineal" refers to descent or inheritance. In a patrilineal system, descent, inheritance, and kinship are traced through the male lineage. This relates to the rule of inheritance. (C) corresponds to (IV).
(D) Nuclear Family: This term describes family unit composition. A nuclear family is the smallest unit, generally consisting of parents and their unmarried offspring. This constitutes one set of parents and their children. (D) corresponds to (I).
Step 3: Conclusion: The correct pairings are: (A)-(II), (B)-(III), (C)-(IV), (D)-(I).