Statements : Some blankets are beds. Some pillows are blankets. All beds are pillows. Conclusions : I. Some blankets are pillows. II. Some pillows are beds. III. Some beds are blankets.

The correct answer is: Only I and either II or III follow.

The first statement, “Some blankets are beds,” can be expressed in propositional logic as $B \subseteq P$. The second statement, “Some pillows are blankets,” can be expressed as $P \subseteq B$. The third statement, “All beds are pillows,” can be expressed as $P \subseteq B$.

The first conclusion, “Some blankets are pillows,” is a direct consequence of the first two statements. The second conclusion, “Some pillows are beds,” is a direct consequence of the second and third statements. The third conclusion, “Some beds are blankets,” is a direct consequence of the third statement.

Therefore, only I and either II or III follow.

Here is a more detailed explanation of each option:

• Option A: Only either I or II follows. This option is incorrect because both I and II follow.
• Option B: Only I and either II or III follow. This option is correct.
• Option C: Only III and either I or II follow. This option is incorrect because I does not follow.
• Option D: All I, II and III follow. This option is incorrect because II does not follow.
• Option E: None of these. This option is incorrect because I and II follow.