Exactly which one?

Logic Level 3

Given below are three statements:

1) If this statement is right, then the second statement is also right.

2)If this statement is right, then first statement is also right.

3)If this statement is correct, then the first statement is wrong.

If exactly one of these statements is correct, which one is it?

First one is correct Second one is correct Third statement is correct This is an impossible scenario

3 solutions

Ashish Menon
Apr 25, 2016

The first is correct then second should also be correct because they are biconditional statements (ie. First is true iff second is true and second is true iff first is true). But as only one of them is correct, we conclude that both first and second statements are lying. So, the only one left is the third statement which has no counter statement and hence speaks the truth. It satisfies all the conditions of the question.

I have trouble interpreting this question. How does "2) If this statement is right, then first is also right" result in " Second statement says that first statement lies"?

Calvin Lin Staff - 5 years, 1 month ago

Sir, the first half of the second statement says some blah blah blah, and the second statement says that the answer "lies" within this statement. By "lies" it seems like he mean that the answer is within this statement, but I believe that by "lies", he meant that he is not being honest.

Ashish Menon - 5 years, 1 month ago

I have no idea what you're saying in the current format. Please edit your solution for clarity, and add in the leaps of logic that you are marking.

IE If the first statement is correct, then the second statement is also correct. Hence this is not possible.

Calvin Lin Staff - 5 years, 1 month ago

@Calvin Lin – I think the second statement has been edited now. Now I get a different solution.

Like first is correct then second also should be correct because they are biconditional statements. But as only one of them is correct, we conclude that both first and second statements are lying. So, the only one left is the third statement which has no counter statement and hence speaks the truth.

Ashish Menon - 5 years, 1 month ago

@Ashish Menon – Yea, that's why I've asked @Abhay Tiwari to write a solution, so that I can understand what he is thinking.

The rest of our discussion is in the report forum.

Calvin Lin Staff - 5 years, 1 month ago

@Calvin Lin – Sir, I guess we should delete the question now because we had a long discussion on this Question and still the question is unclear. It's better to remove it than to create more confusion. I will try to make my questions with more clarity in them. Thanks!

Abhay Tiwari - 5 years, 1 month ago

@Abhay Tiwari – I think the question, as stated now, is fine and clearly written. However, this particular solution is no longer relevant, hence it just needs a solution to explain what you're thinking.

Calvin Lin Staff - 5 years, 1 month ago

@Calvin Lin – Sir, I have published the solution, you can check it

Abhay Tiwari - 5 years, 1 month ago

@Abhay Tiwari – So by lies did you really mean that the answer is present in the statement? I interpreted it as not being honest.

Ashish Menon - 5 years, 1 month ago

@Ashish Menon – yes i really meant it, did you understand the solution in the report section?

Abhay Tiwari - 5 years, 1 month ago

@Abhay Tiwari – Wow, great solution :)

Ashish Menon - 5 years, 1 month ago

@Calvin Lin – I have edited it now :)

Ashish Menon - 5 years, 1 month ago

Mateo Matijasevick
May 12, 2016

Unfortunately, this is an impossible scenario. If only the third statement is true, then the first one and the second are false.

Let's analyze the first statement: if it is false, then its antecedent is true and its conclusion is false. Thus, the first statement is true and the second is false. We already knew that the second statement is false.

Let's analyze the second statement: if it is false, then its antecedent is true and its conclusion is false. Therefore, the second statement is true and the first statement is false.

We have arrived to a contradiction: the first statement is false and is true, as the second. This is impossible cause a statement can only be true or false, but not at the same time both.

Abhay Tiwari
Apr 27, 2016

While solving the Question, we will have to keep in mind that only one of the statement is correct and the rest are false.

Now let's consider the first statememt, it says:

1) If this statement is right, then the second statement is also right

Let's assume that the statement is right. Now, if it is right then it guarantees the correctness of the second statement. But as I said, only one statement is correct, which means that this statement is false.

Now let's move on to the second statement, it says:

2) If this statement is right, then the first statement is also right

Let's assume that the statement is right. Now, if it is right then it guarantees the correctness of the first statement. But as I said, only one statement is correct, which means that this statement is also false.

Now we are left with third statement only, let's check it, it says:

3)If this statement is correct, then the first statement is wrong.

Let's assume that the statement is right. Now, if it is right then it guarantees the falseness of the first statement, which is proving our assumption(for the first and the second statement) right, which means that:

Third statement is right, making the first statement false.
As soon as the first statement goes wrong(which holds the guarantee for the correctness of second statement ), the second statement also goes wrong.

Therefore, the third statement is the only valid option.

I must disagree with you (and agree with Mateo Matijasevick). Let's suppose that (3) is true, and (1) and (2) are false. Since (3) implies that (1) is false, that´s OK. But (2) is equivalent to the statement "if (1) is false, then (2) is false"; since, by hypothesis, (1) and (2) are false, that statement is true --- a contradiction.

Ricardo Moritz Cavalcanti - 10 months, 3 weeks ago

Exactly which one?

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