Logic Question?

Question

3.

You are marooned on an island where there are only liars and truth tellers. You meet a couple and ask the husband, "Are you liars or truth tellers?" Whan can you conclude if he replies as folllows? Explain.
a) If I am a truth teller than so is my life
b) I am a truth teller if and only if my wife is a truth teller

This is logic ? number 3. First person to get it right gets 10 points. Take a guess if your clueless. Show bit of work. For more logic questions go to my profile

wife not life~
sorry for typos.

Answer 1

First, statement a, which I assume should read, "If I am a truth teller then so is my WIFE".

If the husband is truthful, then his wife is also.

If the husband is a liar, then technically, the statement is true because it has a false premise. Just as I would be truthful if I said, "If all the grass is orange, I will give you $5." Therefore, I would say that this cannot be the case because that contradicts the assumption that he is a liar.

So statement (a) would then mean that both are indeed truth tellers.


Now statement b: "I am a truth teller if and only if my wife is a truth teller" claims that both are the same: truth teller or liar.

So if he is truthful, then his wife must be also.
If he is a liar, then the statement must be false, so his wife is a truth teller.

Therefore, we can conclude from statement b that his wife is truthful, although we don't know anything about his own truthfulness.


What do you think of my logic here?

Answer 2

If (a) is true, then both are truth tellers; if not, the husband is a liar. If (b) is true, then both are truth tellers; if not, he is a liar and his wife is not.

The reasoning is as follows:
(a)=true is trivially easy; (a)=false means the speaker is a liar but tells nothing about the other; (b)=true requires that both tell the truth for its truth to stand; (b)=false means the speaker is a liar, and for the wife to be a liar as well would contradict the falsity of (b).

Actually, the "correction" of statement (a) is still incorrect, because it should be "THEN so is my wife"!

Answer 3

a) If I am a truth teller than so is my wife

We may conclude that either both are truthtellers, or else the husband is a liar, with the wife's truthfullness up in the air.

B) If he is a liar and his wife is a truthteller, the statement is true. Not possible.
If he is a liar and his wife is a liar, the statement is true. Not possible.
If he tells the truth, and his wife tells the truth, no problem.
If he tells the truth and his wife is a liar, the statement is false. Not possible.

Consequently, both he and his wife are telling the truth.

Answer 4

That's ok..re: typos.

This is a verrry old, timeless and fun, albeit very easy "logic" question. It has many variations to it but is something my wife has used in her elementary school classes. The puzzle was presented to kids back in the 80's with David Bowie's movie Labyrinth as well.

We love logics here, so keep 'em coming!

Here is another variation:
You approach two magic talking doors. One door leads to the City of Truth, while the other door leads to the City of Liars. You do not know which door is which. You are able to ask only one question to determine which door is which. The door that leads to the City of Liars always speaks lies, while the door that leads to the City of Truth always speaks the truth. You want to go to the City of Truth. What question do you ask to determine which door leads to the City of Truth?

Cheers!

Answer 5

They both have to be truth tellers.

If he was lying he would be lying when he said that he is a truth teller if his wife was. Therefore neither of them can be lying.

Answer 6

They are all liars