All hill-stations have a lake. Ooty has two lakes. Which of the statement(s)…
2016
All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
- A.
(i) only
- B.
(ii) only
- C.
both (i) and (ii)
- D.
neither (i) nor (ii)
Attempted by 64 students.
Show answer & explanation
Correct answer: D
Answer: neither (i) nor (ii).
Given statements in logical form: every hill-station has at least one lake; Ooty has two lakes (so Ooty has at least one lake).
Statement (i): "Ooty is not a hill-station" is not entailed. Knowing that Ooty has a lake (indeed two) does not allow us to conclude it is not a hill-station; it could be a hill-station with two lakes.
Statement (ii): "No hill-station can have more than one lake" is not entailed. The premise only asserts at least one lake for each hill-station; it places no upper bound on the number of lakes a hill-station may have.
Therefore neither statement can be logically inferred from the given information.
A video solution is available for this question — log in and enroll to watch it.