Statements: All squares are rectangles. Some rectangles are circles. Conclusions: I. Some circles are squares. II. Some rectangles are not squares. III. All squares are circles.
Correct answer: A. None follow
- A. None follow
- B. Only II
- C. Only I and II
- D. All follow
Explanation
The statements provide the following information: 'All squares are rectangles' and 'Some rectangles are circles'. Conclusion I, 'Some circles are squares', is not supported because there is no direct connection between circles and squares based on the given information. Conclusion II, 'Some rectangles are not squares', cannot be concluded as all squares are indeed rectangles, but it doesn't imply that some rectangles are not squares. Conclusion III, 'All squares are circles', is not supported because we only know that 'some rectangles are circles' and not all rectangles. Therefore, none of the conclusions follow from the statements.
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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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