All hill-stations have a lake. Ooty has two lakes?

Question

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. $(i)$ only
2. $(ii)$ only
3. both $(i)$ and $(ii)$
4. neither $(i)$ nor $(ii)$

---

My attempt :

Statement $(i)$ can be false, since all hill-stations has lake, but if a city has lakes, that does not mean that city is a hill-station.

For statement $(ii)$, a lake means may be any lake means number is not given. I've not formal way, this statement given false.

Can you explain in formal way, please?

Answer 1

According to the given statements,

All hill-stations have a lake. Ooty has two lakes.

The above statements do not strictly imply any $1$ of the following:

A. All hill-stations have exactly $1$ lake.

B. All hill-stations have atmost a lake.

C. All hill-stations have at least a lake.

$1.$ should be correct if interpretation $C.$ is absolutely true.

$2.$ should be correct if interpretation $B.$ is absolutely true.

$3.$ should be correct if interpretation $A.$ is absolutely true.

But the interpretations as mentioned are not strictly implied. Any $1$ of them might be true but which one ... it has not been stated directly.

Hence $4.$ is correct as it is most logical.