Three desk shelves-I, II, and III-are being stocked with seven types of food. Bread, Biscuits, Pizzas, Shakes, Cake, Sweet, and Sandwich are to be placed in the shelves so that the goods belonging to any given type are all together in one shelf and no shelf contains more than three types of food. The arrangement of the types of food is subject to the following further constraints: Bread and Cake must be in a shelf together. Neither Biscuits nor Shakes can be in the same shelf as Pizzas. Neither Biscuits nor Shakes can be in the same shelf as Sweet. The Sweet must be in either shelf I or shelf II. Each type of goods must be in some shelf or other. If Pizzas are in I and Sweets are in II, which of the following must be true?

Explanation: Foods: B, Bi, P, Sh, C, Sw, Sa. Max 3 foods/shelf. Rules: (1) B & C together. (2) Bi, Sh \(\neq\) P. (3) Bi, Sh \(\neq\) Sw. (4) Sw is in I or II. (5) All foods used. Given: **Pizzas (P) are in I** and **Sweet (Sw) is in II**. Shelf I = {P}, Shelf II = {Sw}. Rule (3) \(\implies\) Bi, Sh \(\neq\) Sw. Since Sw is in II, Bi and Sh \(\neq\) II. Rule (2) \(\implies\) Bi, Sh \(\neq\) P. Since P is in I, Bi and Sh \(\neq\) I. Thus, Bi and Sh must be in **Shelf III**. Shelf III = {Bi, Sh}. Remaining food: {B, C, Sa}. Remaining shelves: I, II. Rule (1) \(\implies\) B & C together. B & C must be in one shelf. B & C \(\neq\) III (max 3, already has 2, B or C would put it over 3). B & C can be in I or II. If B & C in I: Shelf I = {P, B, C} (3 items). Shelf II = {Sw} (1 item). Sa must be in II. Shelf II = {Sw, Sa} (2 items). All rules satisfied. If B & C in II: Shelf II = {Sw, B, C} (3 items). Shelf I = {P} (1 item). Sa must be in I. Shelf I = {P, Sa} (2 items). All rules satisfied. The only statement that **must** be true based on the initial placement and rules (2) and (3) is that **Biscuits are in III**.