Difficulty: Easy
Correct Answer: uncertain
Explanation:
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:
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:
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:
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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