Question

question{logical reasoning)

My next door neighbour lies a lot...

Answer 1

b) is possible

Answer 2

how

Answer 3

1) Lie on Mon. and Tue.
2) Today is Wed or Sat or Sun
3) Lie on Wed and Fri

If 3) is true, then others are false. In particular, 1) is false. Therefore 3) has been said on Mon or Tue.
If 2) has to be false, the only possibility is that the truth is told on Tue so that 2) was told on Monday, which makes 2) false as well.

Answer 4

The second option is either thurs, sat or sun

Answer 5

okay...
hm, but it still works! :-)

Answer 6

so what's the day when she said the first statement?

Answer 7

Sunday

Answer 8

that may be the day he tells the truth

Answer 9

No contradiction
Sunday makes the first statement false which makes the second statement false

Answer 10

No, because [Lie on Mon and Tue] and [Lie on Wed and Fri] cannot both be correct

Answer 11

If first statement is false, which means she doesnt lie on Moday which means she isnt going to lie on the monday, second statement

Answer 12

1) false doesn't imply Truth on Monday. Could be on Tuesday.

Answer 13

1 says he doesn't lie on MONDAYS AND on TUESDAYS. So the next day is Monday which should be the day she is going to say the truth. But according to you, she says truth on tuesday.

Answer 14

What is 1) for you?

Answer 15

you mean which day is 1 for me?

Answer 16

What is the Day of 1) and the phrase 1) itsself.

Answer 17

I am not sure about the day, still working out the possibilities

Answer 18

Wait a minute one day a week can mean that he will say truth on sat , lie on sun and say truth again on monday(next week)?

Answer 19

Yes, but the phrases are told on 3 consecutive days.

Answer 20

saturday, the next day sunday the next day monday

Answer 21

but that will give different answers for "truth" days so that cant be a posssibility

Answer 22

I didn't understand. What is the day of Truth for you, with Sat-Sun-Mon talking days?

Answer 23

saturday and monday both

Answer 24

The statement says that "my neighbour only tells the truth on one day of the week". Maybe you missed this

Answer 25

You didn't get my point but still my theory will give many answers so cant be what the question is asking

Answer 26

None of these and Saturday is the day he says truth

Answer 27

and the first day?

Answer 28

Thursday

Answer 29

then 1) is a lie, which means the truth is told on Mon or Tue. Not on Saturday.

Answer 30

Not in this week

Answer 31

hehe..

Answer 32

Becuase either the first statement is going to be true or the third one and they will keep contradicting each other if followed through your logic

Answer 33

I don't see the contradiction in my answer. (which was Truth on Tuesday, first day is Sunday)

Answer 34

@mathmath333 intervention?

Answer 35

First satement say I say truth on monday (since it get falsified)
The next day is Monday, thus she has to say the truth
The next day is Tuesday and according to you thats the truth day
Thus two days can't be truth days

Answer 36

in book answer given is tuesday

Answer 37

IF "Lie on Monday and Tuesday" is false, that doesn't mean that BOTH Monday and Tuesday are days of Truth. Just one of them is enough.

Answer 38

and there can be only one. So I tested with Tuesday and it worked.

Answer 39

But that will give many answers

Answer 40

This is true:
not (lie on Mon and Tue) == (truth on Mon) OR (truth on Tue)

This is not true:
not (lie on Mon and Tue) == (truth on Mon) AND (truth on Tue)

Answer 41

how did u concluded that only statement 3 is correct

Answer 42

can't i assume all statements 1 2 3 false

Answer 43

I started with "1) and 3) can't be both true or both false.
So 1) is true or 3) is true. I tested 3): truth on Mon or Tue. To make 2) false, starting day must be Sun.
It works. and I checked other answers do not work.

Answer 44

And even Thurs, Fri, Sat (truth) doesnt provide any logical contradiction

Answer 45

1) and 3) are not both true: because the neighbour tells truth only once.
1) and 3) are not both false: bceause that would make at least two days with truth.

Answer 46

@mathmath333 1 2 3 all false would mean 1) and 3) false : there is a truth-day in Mon-Tue, and there is a truth-day in Wed-Fri. impossible.

Answer 47

how can u contradict if statement 1 2 3 are F F T and truth day is saturday

Answer 48

No there is no contradiction but I think they are just concerned with monday tuesday and wednesday

Answer 49

@mathmath333
1) on Thur
2) on Fri
3) on Sat (true)
Like this?

Answer 50

yes

Answer 51

^

Answer 52

Sicne he lies on Thursday (he MUST because it is not Saturday), then "Lie on Mon and Tue" is a lie.
=> he tells the truth on Monday, OR he tells the truth on Tuesday.
Either way, that makes it a second day for telling the truth.

Answer 53

what????

Answer 54

Friday is the next day

Answer 55

In your example, 1) is said on Thursday?

Answer 56

Yes

Answer 57

Do you agree that it is a lie ?

Answer 58

Ofcourse

Answer 59

He has pronounced "I lie on Monday and Tuesday" on that day. Still ok ?

Answer 60

Hmm can you do it a little fast

Answer 61

If I do it fast, you don't agree with me.

Answer 62

the negation of "I lie on Monday and Tuesday" is " either i say truth on monday or tuesday"

is it correct

Answer 63

1.) Lie on Moday and tuesday--->Truth on monday and tuesday
2) Today is thursday and since he is lying (cause Friday) no contradiction
3) I lie on Wednesday and Friday. No contradiction arises since Saturday and is telling the truth

Answer 64

I am pretty sure it's just because they are concerned with the first three days of the week.

Answer 65

"Truth on monday and tuesday" this contrdicts with the idea that the neighbour lies only once a week

Answer 66

No it means that he tells truth on some weeks monday and on some weeks tuesday

Answer 67

If ["Lie on Mon and Tue"] is a lie, then the negation of it is true.
The negation of "lie on Mon AND lie on Tue is "truth on Mon OR truth on Tue".

At least one of those days is truth-day. Therefore, Mon/Tue + Saturday makes 2 days of truth.

Answer 68

It cannot vary accross weeks... that's cheating :)

Answer 69

We can sum this up like this:
Day 1: statement1 = "I lie on Mondays and on Tuesdays"
Day 2: statement2 = "Today is either Thursday, Saturday or Sunday"
Day 3: statement3 = "I lie on Wednesdays and Fridays"
We have two possibilities, the first one is that these three days don't contain the day in which he tells the truth, and the second is that one of these three days is the day in which he tells the truth.
If the first possibility is correct then statement1 and statement2 are false. i.e { he tells the truth in Mondays or Tuesdays } AND { he tells the truth in Wednesdays or Fridays }. Meaning there are two days in the week in which he tells the truth. #contradiction
Which leaves us with possibility #2.
There are three choices of days in which he tells the truth: Day 1 or Day 2 or Day 3.
Suppose he tells the truth in day 1.
Then Day 1 is not Monday nor Tuesday.
Statement2 is false then Day 1 is neither Wednesday nor Friday nor Saturday.
So day 1 (the day in which he tells the truth) is either Thursday or Sunday
Statement3 is false so he tells the truth in either Wednesdays or Fridays. #contradiction
Now Suppose he tells the truth in day 2.
Statement1 is false so he tells the truth in either Mondays and or Tuesdays.
Statement2 is true then today (the day in which he tells the truth is either Thursday, Saturday or Sunday). #contradiction
Finally suppose he tells the truth in Day 3.
He tells the truth in Mondays or Tuesdays (ie day 3 is either Monday or Tuesday)
Day 2 is not Thursday, Saturday or Sunday (ie day 3 is NOT Friday, Sunday, or Monday)
Hence the day in which he tells the truth is Tuesday.

Answer 70

i think is monday and thrusday