search
Log In
10 votes
2k views

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?

  1. Ooty is not a hill-station.
  2. 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)
in Verbal Aptitude
edited by
2k views

2 Answers

21 votes
 
Best answer

All hill stations have a lake  $\Rightarrow  \forall x( h(x)\to (\exists y, l(y) \wedge has(x,y)))$

Ooty has two lakes $\Rightarrow \exists x ( o(x) \wedge \exists y,z ( has(x,y,z)\wedge l(y)\wedge l(z)\wedge (z!=y) )$ 

Here, $h(x) \to x \text{ is hill station}$

  • $l(x) \to x \text{ is lake }$
  • $has(x,y)\to x \text{ has }y$
  • $has(x,y,z)\to x\text{ has } y, z$
  • $o(x)\to x \text{ is Ooty}$
  1. Ooty is not a hill station $\implies$ we can not derive this above arguments, Ooty has two lakes already, if Ooty had $0$ lakes only then this can become true.
  2. No hill station can have more than one lake

All arguments here are saying are if we have hill station, it can have lake. It is nowhere told that how many lakes it has. So, this is false.

Answer: (D) neither (i) nor (ii)


edited by
0
Also, there could exist some places which have lakes but those place might not be a hill station.

$(could\ be\ True \ or\ false)?\rightarrow Has\ a\ lake(give\ as\ true ) \\ don't\ goes\ backward\leftarrow True$

only false goes backward.

so we can't say if a place has "two lakes"(basically "having a lake" condition is true) is a hill station or not because both are possible.$$0\ 0\ T \\{\color{Green} 1}\ {\color{Red} 1}\ T \\1\ 0\ F \\{\color{Yellow} 1}\ {\color{Red} 1}\ T$$
4 votes
Every hill station has a lake means "every hill station has at least one lake". That means a hill station can have more than one lakes. But, a place without any lake cannot be a hill station. So, none can be concluded.
Answer:

Related questions

1 vote
2 answers
1
611 views
All people in a certain island are either 'Knights' or 'Knaves' and each person knows every other person's identity. Knights never lie, and Knaves ALWAYS lie. $P$ says "Both of us are Knights". $Q$ says "None of us are Knaves". Which one of the following can be logically inferred ... . $P$ is a knight; Q is a Knave. Both $P$ and $Q$ are Knaves. The identities of $P, Q$ cannot be determined.
asked Feb 27, 2017 in Verbal Aptitude Arjun 611 views
4 votes
2 answers
2
1k views
All professors are researchers Some scientists are professors Which of the given conclusions is logically valid and is inferred from the above arguments: All scientists are researchers All professors are scientists Some researchers are scientists No conclusion follows
asked Feb 16, 2016 in Verbal Aptitude Akash Kanase 1k views
3 votes
2 answers
3
1.3k views
Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows. Statements: No manager is a leader. All leaders are executives. Conclusions: No manager is an executive. No executive is a manager. Only conclusion I follows. Only conclusion II follows. Neither conclusion I nor II follows. Both conclusions I and II follow.
asked Feb 15, 2016 in Verbal Aptitude Akash Kanase 1.3k views
4 votes
1 answer
4
1.3k views
Find the odd one in the following group of words. mock, deride, praise, jeer Mock Deride Praise Jeer
asked Feb 12, 2016 in Verbal Aptitude Akash Kanase 1.3k views
...