Question at position 23 Which of the following statements is true about the figure shown below? A rental unit must be either an apartment or a house, and could be both.A rental unit can be an apartment, house or just a rental unit; it may not be more than one at the same time.A rental unit can be an apartment, a house or just a rental unit. It could be both an apartment and a house at the same time.A rental unit must be either an apartment or a house, and cannot be both at the same time.

Question

BlackTom AI · Accepted Answer

The diagram shows a large rectangle labeled "rental unit" containing two interior regions labeled "apartment" and "house" that do not overlap, plus an area inside the rectangle but outside both regions.

1) Relevant knowledge points and concepts
- Venn diagram interpretation: a rectangle is the universal set (here: all rental units); interior shapes (circles/ovals) are subsets (apartments, houses). 
- Overlap between subsets indicates elements that belong to both categories; non-overlapping subsets indicate mutually exclusive categories. 
- Area inside the rectangle but outside all subset shapes represents items that are rental units but neither apartments nor houses.

2) Step-by-step reasoning
- Identify the universal set: the rectangle = all rental units.
- Identify subsets: the two distinct interior regions represent apartments and houses.
- Note spatial relationship: the apartment and house regions do not intersect (no shared area).
- Note the existence of rectangle area outside both subsets: there are rental units that are neither apartments nor houses.

3) Intermediate logical steps
- If there were overlap between apartment and house regions, some rental units could be both apartment and house; the diagram has no overlap, so no rental unit belongs to both categories.
- Because of the area of the rectangle outside both subsets, being a rental unit does not force membership in either subset; some rental units are "just rental units" (neither apartment nor house).

4) Why the correct answer is correct
- The statement "A rental unit can be an apartment, house or just a rental unit; it may not be more than one at the same time." exactly matches the diagram: three possibilities (apartment only, house only, neither) and mutual exclusivity between apartment and house (no overlap).

5) Why other options are incorrect
- Option 1 ("must be either an apartment or a house, and could be both"): incorrect because the diagram shows rental units outside both subsets (so not every rental unit must be one of those), and there is no overlap to allow "both."
- Option 3 ("could be both an apartment and a house at the same time"): incorrect because apartment and house regions do not overlap.
- Option 4 ("must be either an apartment or a house, and cannot be both at the same time"): incorrect because it omits the region of rental units that are neither apartment nor house (the diagram shows such a region).

Conclusion: The diagram supports the provided answer: "A rental unit can be an apartment, house or just a rental unit; it may not be more than one at the same time."

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