Question 1
Given Conclusion:
Some squares are shapes
Which set of statements can definitely lead to this conclusion?
A. All squares are rectangles; Some rectangles are shapes
B. All tables are rectangles; Some random are shapes
C. No squares is a shapes; All squares are rectangles
D. Insufficient information
Reverse Syllogism Analysis:
Working backwards from conclusion to verify which premises support it.
Given Conclusion: Some squares are shapes
Testing Option A: All squares are rectangles; Some rectangles are shapes
Applying syllogism rules:
Statement 1: All squares are rectangles
Statement 2: Some rectangles are shapes
Combining these gives: Some squares are shapes ✓
Why Other Options Fail:
B. Random statements: No logical connection to conclusion
C. Opposite relationships: Would give contradictory conclusion
D. Insufficient: We CAN determine with proper analysis
Answer: A. All squares are rectangles; Some rectangles are shapes
Working backwards from conclusion to verify which premises support it.
Given Conclusion: Some squares are shapes
Testing Option A: All squares are rectangles; Some rectangles are shapes
Applying syllogism rules:
Statement 1: All squares are rectangles
Statement 2: Some rectangles are shapes
Combining these gives: Some squares are shapes ✓
Why Other Options Fail:
B. Random statements: No logical connection to conclusion
C. Opposite relationships: Would give contradictory conclusion
D. Insufficient: We CAN determine with proper analysis
Answer: A. All squares are rectangles; Some rectangles are shapes