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.
Answer: II
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.
