Statements: (1) All squares are rectangles. (2) All rectangles are polygons.
Conclusions:
I. All squares are polygons.
II. Some polygons are squares.
Which conclusion(s) logically follow?
Answer and explanation
Correct answer: A. Both conclusions I and II follow
- Step 1: By transitive deduction of universal affirmatives (Barbara syllogism): All squares are rectangles and all rectangles are polygons All squares are polygons. Conclusion I definitely follows.
- Step 2: Since All squares are polygons, by conversion: Some polygons are squares. Conclusion II definitely follows.
- Step 3: Both conclusions follow logically.
Answer
Both conclusions I and II follow.
Why not the others: Both statements are universally valid deductive consequences of subset transitivity, so choosing only one conclusion is incomplete.
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