All hammers are tools. Some tools are useless things. All useless things are trash. Which of the following is NECESSARILY TRUE given only the information above?ConclusionsI. Some hammers are trash. II. Some tools are trash.III. All useless things are tools.
Correct answer: D. II
- A. I and III
- B. I and II
- C. II and III
- D. II
Explanation
Now look at the conclusions provided, For I, if we look at the diagram some hammers are not trash hence I is wrong. For II, Some tools are trash as indicated in the yellow-shaded region hence II is correct. For III, Not ALL useless things are tools rather some useless things are tools so III is also wrong. The only option correct according to the above analyses is D ( only conclusion II).
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About Syllogisms
Syllogisms use categorical statements such as all, some and no to establish relationships between groups. Questions require checking whether conclusions necessarily follow from the premises, often by mental set relationships or Venn diagrams, and distinguishing valid deductions from conclusions that are merely possible.
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