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All hammers are tools. Some tools are useless things. All useless things are trash. Which of the following conclusions is NECESSARILY TRUE given only the information above? CONCLUSIONS: I. Some hammers are trash II. Some tools are trash III. All useless things are tools.
  1. II
  2. I
  3. III
  4. I&III
Explanation

Based on the statements:

  • Since some tools are useless things and all useless things are trash, it follows that some tools must be trash.
  • Conclusion I cannot be confirmed as we do not know if any hammers fall into the category of tools that are trash.
  • Conclusion III is false because not all useless things are tools.

Thus, only II is necessarily true.

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