Statements: I) A regular polygon has equal sides and equal angles. II) A square is a regular polygon. Conclusions: I) A square has equal sides. II) A square has equal angles.
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AConclusion I follows.
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BConclusion II follows.
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CNeither I nor II follows.
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DConclusions I and II both follow.
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ENone of these
Answer
Correct Answer: Conclusions I and II both follow.
Explanation
Introduction / Context:This is a direct syllogism using class membership and inherited properties: square ∈ regular polygons; regular polygons have equal sides and equal angles.
Given Data / Assumptions:
- All regular polygons: equal sides & equal angles.
- Square is a regular polygon.
Concept / Approach:Properties of a class apply to its members. Therefore, any square inherits the defining properties of a regular polygon.
Step-by-Step Solution:1) From I: Regular polygon → equal sides and equal angles.2) From II: Square → regular polygon.3) Therefore: Square → equal sides (Conclusion I) and equal angles (Conclusion II).
Verification / Alternative check:Independent geometric knowledge corroborates the same; but the logical chain alone suffices.
Why Other Options Are Wrong:Choosing only one conclusion arbitrarily discards the other inherited property; “neither” contradicts the explicit inheritance.
Common Pitfalls:Overthinking or introducing exceptions that do not exist in the definition of “regular.”
Final Answer:Both Conclusions I and II follow.