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Select the correct answerStatements:Some pens are pencils.Some pencils are not erasers.Conclusions:I. All erasers are pens.II. Some erasers are not pens.OptionsIf only conclusion I followsIf either conclusion I or conclusion II followsIf both conclusion I and conclusion II followsIf neither conclusion I nor conclusion II followsIf only conclusion II follows

Question

Select the correct answerStatements:Some pens are pencils.Some pencils are not erasers.Conclusions:I. All erasers are pens.II. Some erasers are not pens.OptionsIf only conclusion I followsIf either conclusion I or conclusion II followsIf both conclusion I and conclusion II followsIf neither conclusion I nor conclusion II followsIf only conclusion II follows

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Solution

The correct answer is "If only conclusion II follows".

Here's the step by step reasoning:

  1. The first statement says "Some pens are pencils." This means there is an overlap between pens and pencils.

  2. The second statement says "Some pencils are not erasers." This means there is a part of pencils that doesn't overlap with erasers.

  3. Conclusion I says "All erasers are pens." Based on the statements, we cannot confirm this. We only know that some pencils (which could also be pens) are not erasers. We don't have information about all erasers being pens.

  4. Conclusion II says "Some erasers are not pens." This could be true. Since some pencils are not erasers, and some of these pencils could be pens, it's possible that some erasers are not pens.

Therefore, only conclusion II follows the given statements.

This problem has been solved

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