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.

  1. A.

    (i) only

  2. B.

    (ii) only

  3. C.

    both (i) and (ii)

  4. D.

    neither (i) nor (ii)

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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.

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