Direction: Read the following statements and conclusions and choose the…
2024
Direction: Read the following statements and conclusions and choose the correct option from the choices given below. Statements: I) All Pens are Balls. II) All Balls are Tables. III) Some Tables are Chairs. Conclusions: I) Some Chairs are Tables. II) Some Balls are Chairs. III) Some Chairs are Pens.
Answer: A. Only conclusion I is correct — Concept: In syllogisms, a particular affirmative statement of the form 'Some A are B' always converts directly to 'Some B are A' — this is a guaranteed…
- A.
Only conclusion I is correct
- B.
Only conclusion III is correct
- C.
Both conclusion I and II are correct.
- D.
None of the conclusions is true.
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Correct answer: A
Concept: In syllogisms, a particular affirmative statement of the form 'Some A are B' always converts directly to 'Some B are A' — this is a guaranteed immediate inference that needs no further assumption. By contrast, a 'Some' relationship can never be pushed through a chain of universal ('All') statements to force a new specific overlap with an inner circle — if even one valid Venn diagram satisfying all the given statements makes a conclusion false, that conclusion does not follow.
'All Pens are Balls' and 'All Balls are Tables' place the Pens circle inside the Balls circle, which sits inside the Tables circle (Pens ⊆ Balls ⊆ Tables); so every Pen is automatically also a Table.
'Some Tables are Chairs' means the Tables and Chairs circles overlap somewhere. The statements give no reason for that overlap to reach the Balls or Pens circles, so the minimum valid diagram draws the Tables-Chairs overlap entirely in the outer 'Tables-only' region, away from Balls and Pens.
Conclusion I ('Some Chairs are Tables') is simply the converse of 'Some Tables are Chairs' — a particular affirmative statement always converts, so this holds in every possible diagram that satisfies the given statements.
Conclusion II ('Some Balls are Chairs') would require the Tables-Chairs overlap to intersect the Balls circle — but the minimum diagram above keeps them separate, so a valid diagram exists where this conclusion is false.
Conclusion III ('Some Chairs are Pens') would require the overlap to reach the innermost Pens circle — again nothing in the statements forces this, so a valid diagram exists where this conclusion is also false.
Cross-check: Since Conclusions II and III each fail in at least one valid diagram while Conclusion I holds in every valid diagram (by direct conversion of the given 'Some' statement), only Conclusion I is a definite conclusion.
Result: Hence, only Conclusion I is correct.