Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusion can be deduced from the preceding sentences? i. At least one bench is a table ii. At least one shelf is a bench iii. At least one chair is a table iv. All benches are chairs A. Only i B. Only ii C. Only ii and iii D. Only iv

GATE 2017 · General Aptitude · Statements Follow · medium

Answer: Only conclusion ii is a guaranteed deduction. Answer: B. Only ii.

1. Test conclusion ii: At least one shelf is a bench: Premise 2 says some shelves ARE chairs. Premise 3 says ALL chairs ARE benches. So those shelves that are chairs must also be benches (by Premise 3). Therefore at least one shelf is a bench. Conclusion ii HOLDS.
2. Test conclusions i, iii, iv: i: Some tables are shelves, but we cannot chain further to benches because the shelf-chair overlap may not include those shelves that are also tables. Conclusion i is NOT guaranteed. iii: Some shelves are chairs, but the tables that are shelves need not be the same shelves that are chairs, so no chair must be a table. Conclusion iii is NOT guaranteed. iv: All chairs are benches does NOT mean all benches are chairs (conversion fallacy). Conclusion iv is INVALID.