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)

GATE 2016 · General Aptitude · Statements Follow · easy

Answer: D. Neither (i) nor (ii)

1. Translate the premise formally: Premise: forall x (HillStation(x) -> HasALake(x)). This means every hill-station has at least one lake. It does NOT say exactly one lake.
2. Check inference i: Ooty is not a hill-station: The premise says hill-stations have a lake. Ooty has two lakes, which satisfies 'has a lake'. There is no rule that having two lakes makes a place not a hill-station. Inference i is INVALID.
3. Check inference ii: No hill-station can have more than one lake: Inference ii adds a maximum restriction. The premise only gives a minimum (at least one lake). No maximum is stated. Inference ii is INVALID.
4. Conclude: Both inferences are invalid. Answer is D: Neither (i) nor (ii).