Spatial reasoning — relative positions of a store, a pharmacy, and a house Statements: • The Shop and Save Grocery is south of Greenwood Pharmacy. • Rebecca's house is northeast of Greenwood Pharmacy. Question: If the first two statements are true,.

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Solve this multiple-choice question and choose the correct option.

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Introduction / Context:This problem examines qualitative spatial reasoning on a grid. Directions like south and northeast constrain relative positions but still leave degrees of freedom. The objective is to decide whether the third statement must hold, given only the first two constraints. Given Data / Assumptions: Let the pharmacy be the origin (0, 0) on an x–y plane. “South of the pharmacy” means the store has y < 0 (x can be any real value). “Northeast of the pharmacy” means the house has x > 0 and y > 0. “West of the store” means the house's x-coordinate is less than the store's x-coordinate. Concept / Approach:We translate each directional statement into coordinate inequalities. If there exist valid placements satisfying the first two statements where the third is true, and also valid placements where the third is false, then the third statement is not determined by the premises and is therefore “uncertain”. Step-by-Step Solution: Place the pharmacy at (0, 0) without loss of generality.Constraint 1: Store S has coordinates (xs, ys) with ys < 0; xs is unconstrained.Constraint 2: House H has coordinates (xh, yh) with xh > 0 and yh > 0.Test a model where the claim is true: Let S = (10, −1), H = (1, 1). Then xh = 1 < xs = 10, so H is west of S. All constraints satisfied.Test a model where the claim is false: Let S = (−10, −1), H = (1, 1). Now xh = 1 > xs = −10, so H is east of S. All constraints still satisfied. Verification / Alternative check:Because both countermodels satisfy the premises but yield opposite truth values for the third statement, the third statement does not necessarily follow; it is indeterminate from the given information. Why Other Options Are Wrong: true or false: each claims a single necessary outcome, but we have consistent scenarios delivering the opposite result. both true and false / none of these: distractors; the correct logical classification is “uncertain”. Common Pitfalls:Assuming “south of” also fixes the x-position (it does not), or assuming “northeast” implies a specific distance or alignment. Only directional quadrants are constrained, leaving room for multiple configurations. Final Answer:uncertain

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