The correct answer is: Only I and III follow.
The first statement, “Some pictures are frames,” can be expressed in propositional logic as $p \subseteq q$. The second statement, “Some frames are idols,” can be expressed as $q \subseteq r$. The third statement, “All idols are curtains,” can be expressed as $r \subseteq s$.
The first conclusion, “Some curtains are pictures,” can be derived from the first and second statements by the rule of transitivity. The second conclusion, “Some curtains are frames,” cannot be derived from the given statements. The third conclusion, “Some idols are frames,” can be derived from the second and third statements by the rule of transitivity.
Therefore, only the first and third conclusions follow.
Here is a more detailed explanation of each option:
- Option A: Only I and II follow. This option is incorrect because the second conclusion, “Some curtains are frames,” cannot be derived from the given statements.
- Option B: Only II and III follow. This option is incorrect because the first conclusion, “Some curtains are pictures,” can be derived from the given statements.
- Option C: Only I and III follow. This option is correct because the first and third conclusions can be derived from the given statements.
- Option D: All follow. This option is incorrect because the second conclusion, “Some curtains are frames,” cannot be derived from the given statements.
- Option E: None of these. This option is incorrect because the first and third conclusions can be derived from the given statements.