Statements: Some radios are televisions. Some televisions are phones. All phones are computers. Conclusions I: All computers being televisions is a possibility. Conclusion II: Some radios being phones is a possibility.

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Accepted Answer

Let $R$ = radios, $T$ = televisions, $P$ = phones, $C$ = computers.

Statements (taken as true):
1. Some $R$ are $T$.
2. Some $T$ are $P$.
3. All $P$ are $C$.

Step-by-step reasoning:

1. Conclusion I: "All computers being televisions is a possibility" (i.e., could all $C$ be subset of $T$?). If all $C$ are $T$, then in particular all $P$ (since $P\subseteq C$) would also be within $T$. This is consistent with statement 2 (some $T$ are $P$) and does not contradict statement 1. No given statement forbids $C$ being entirely inside $T$. Therefore conclusion I is possible.

2. Conclusion II: "Some radios being phones is a possibility" (i.e., could some $R$ overlap with $P$?). We have some $R$ overlapping $T$ and some $T$ overlapping $P$. It is possible to arrange the overlaps so that the same region of $T$ that overlaps $R$ also overlaps $P$, producing some $R$ that are $P$. Nothing in the premises forbids such an overlap. Therefore conclusion II is possible.

Both conclusions I and II are therefore possible given the statements, so the correct choice is option D.

FINAL_ANSWER: d

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