Question

Select the alternative that logically follows the two given statements:
Some rocks are not tables.
Some rocks are balloons.

• A. Some tables are not balloons
• B. Some tables are balloons
• C. Some balloons are not tables
• D. None of the above

Hint:

Both statements use the word some, and two particular statements sharing a common term never force a definite conclusion.

Answer 1

The Correct Option is D

A quicker way to see this is by drawing overlapping circles for rocks, tables and balloons and checking whether every valid diagram agrees on one conclusion.

1. Draw a circle for rocks. Some rocks are not tables means part of the rocks circle lies outside the tables circle, but it does not say how large the tables circle is or where exactly it sits relative to rocks.
2. Some rocks are balloons means part of the rocks circle overlaps with a balloons circle, but again it does not fix the size or position of the balloons circle beyond that one overlap.
3. Draw one valid diagram where the part of rocks that is not tables and the part of rocks that is balloons are two completely separate slices of the rocks circle, with tables and balloons circles not touching each other at all. This diagram satisfies both given statements perfectly.
4. In this diagram, none of the three options hold, since tables and balloons have no connection whatsoever.
5. Now draw a second valid diagram where the balloons circle is placed so that it overlaps only with the part of rocks that is not tables. This diagram also satisfies both given statements, and here some balloons are not tables happens to look true.
6. Since one valid diagram makes all three options false and another valid diagram makes one of them look true, no single option is forced to be true across every diagram that fits the given statements.
7. Because a valid conclusion must hold in every possible diagram consistent with the premises, and here that is not the case for any of the three positive options, the correct choice is None of the above.