GATE EC 2017 Set 1 — Question 60
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General Aptitude → Analytical Aptitude → Deduction & Induction
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Question
Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusions 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
ii. At least one shelf is a bench
iii. At least one chair is a table
iv. All benches are chairs
Correct answer
(B) Only ii
Solution
Let represent the sets of tables, shelves, chairs, and benches respectively.
Given:
i. : Not necessarily true. There is no direct information linking tables and benches.
ii. : True. Since some shelves are chairs () and all chairs are benches (), the intersection must contain , which is non-empty.
iii. : Not necessarily true. There is no direct information linking chairs and tables.
iv. : Not necessarily true. While all chairs are benches, the reverse is not necessarily true.Thus, only conclusion ii is correct.
Given:
1. (Some tables are shelves)
2. (Some shelves are chairs)
3. (All chairs are benches)
Evaluating conclusions:i. : Not necessarily true. There is no direct information linking tables and benches.
ii. : True. Since some shelves are chairs () and all chairs are benches (), the intersection must contain , which is non-empty.
iii. : Not necessarily true. There is no direct information linking chairs and tables.
iv. : Not necessarily true. While all chairs are benches, the reverse is not necessarily true.Thus, only conclusion ii is correct.
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