Three Statements are given followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.

Statement I: All circles are spheres.
Statement II: All spheres are cones.
Statement III: No cone is a cube.

Conclusion I: All circles are cones.
Conclusion II: No sphere is a cube.

1. A

   Only conclusion I follows

2. B

   Only conclusion II follows

3. C

   Both conclusions I and II follow

4. D

   Neither conclusion I nor II follows

Appeared in: MP NHM CHO-2024 (Shift-2)

Explanation

• This option is correct because both conclusions are valid logical deductions derived from the given statements.
• Conclusion I (All circles are cones) is derived by combining Statement I (All circles are spheres) and Statement II (All spheres are cones) through a transitive relationship.
• Conclusion II (No sphere is a cube) is derived by combining Statement II (All spheres are cones) and Statement III (No cone is a cube). Since spheres are a subset of cones, and cones are entirely separate from cubes, spheres must also be separate from cubes.

Why Other Options Were Wrong

• Option A: This option is incorrect because it fails to acknowledge that Conclusion II is also a valid deduction from the statements.
• Option B: This option is incorrect because it fails to acknowledge that Conclusion I is also a valid deduction from the statements.
• Option D: This option is incorrect because, as demonstrated, both Conclusion I and Conclusion II are logically sound deductions based on the provided statements.

Related Visual

• Visual 1: Venn Diagram - A diagram showing three concentric circles labeled 'Circles', 'Spheres', and 'Cones' (with 'Circles' being the innermost). A separate, non-overlapping circle labeled 'Cubes' would be shown to visualize the relationships and confirm the conclusions.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Syllogism and Logical Deduction as background academic context rather than a clinical decision trigger.
• While not a clinical question, this type of logical reasoning is a fundamental skill for nurses.
• Nurses use deductive reasoning to connect patient symptoms (statements) to potential diagnoses (conclusions), follow protocols, and make safe, logical decisions in patient care.
• What if? - If Statement III were 'Some cones are cubes', then Conclusion II ('No sphere is a cube') would no longer be certain. It would be possible, but not guaranteed, that a sphere (which is a cone) could also be a cube.

How to Approach the Question

• First, treat the statements as absolute truths, even if they contradict common knowledge.
• Translate each statement into a logical relationship. 'All A are B' means A is a subset of B. 'No A is B' means the sets A and B are disjoint.
• For Conclusion I, check if you can form a logical chain from 'circles' to 'cones' using the statements. (Circle -> Sphere -> Cone).
• For Conclusion II, check the relationship between 'spheres' and 'cubes'. Since all spheres are cones, and no cone is a cube, determine if there can be any overlap.
• Evaluate each conclusion independently based on the logical chains you've established.
• Select the option that accurately reflects the validity of both conclusions.

Concept Tested & Keywords

• Concept Tested: Syllogism and Logical Deduction
• Stem keywords: Statements, Conclusions, logically follow
• Lead-in keywords: decide which of the conclusions logically follow(s)

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