Statements: All coins are metal. Some metals are silver. Conclusions: I. Some coins are silver. II. Some metals are coins.
Correct answer: D. Only II
- A. Both
- B. Only I
- C. None
- D. Only II
Explanation
To determine which conclusions logically follow from the given statements, we can visualize the relationships using a Venn diagram. The statement 'All coins are metal' suggests that the set of coins is entirely within the set of metals. The statement 'Some metals are silver' suggests there is an overlap between metals and silver. Conclusion II, 'Some metals are coins,' is valid because if all coins are metals, it logically follows that some portion of metals is indeed coins. Conclusion I, 'Some coins are silver,' is not valid because the overlap between metals and silver does not necessarily include any coins. Therefore, only conclusion II follows.
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About Logical Deductions
Logical deductions require conclusions to be drawn from stated facts, conditions and relationships without adding outside information. The work includes handling all, some and none statements, necessary and sufficient conditions, ordering restrictions, true or false conclusions, and the difference between what must be true and what could be true.
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