Which is the correct statement?

I think the easiest method is to just go through each possible answer:

If $(1)$ is true, then $(2)$ is also true, but $(1)$ and $(2)$ contradict each other.

If $(2)$ is true, then $(3)$ is false; however, $(3)$ must be true because $(2)$ is the only true statement above it.

If $(3)$ is true, then one of $(1)$ and $(2)$ must be true also, a contradiction from the assumption that only $1$ statement is true.

If $(4)$ is true, then all of the statements above it are true, a contradiction from the assumption that only $1$ statement is true.

If $(5)$ is true, then all the ones above it must be false. Going through each one, we find that they all hold false.

So $\boxed{5}$ is our answer.

By dividing cases, we can easily solve this problem.

$Cases 1$ : Statement (1) is correct

Statement (1) says that every statement below is correct. Thus, statement (1) implies that point (2) is also correct. But point (1) and (2) are impossible to hold at once. Since statement (1) and (2) are contradicting. Conclution: statement (1) is incorrect.

$Cases 2$ : Statement (2) is correct

If statement (2) is correct then statement (3) to (5) aren't correct. Thus only one of two statements--statement (1) or (2)--is correct. This condition is the same as cases 1. Conclution: Statement (2) is incorrect

$Cases 3$ : Statement (3) is correct

Statement (3) says (again) that only one of two statements--(1) or (2)-- is correct. Conclution (clearly): Statement (3) is incorrect.

$Cases 4$ : Statement (4) is correct

We don't have to discuss this any longer. It is clearly that statement (4) is incorrect

$Cases 5$ : Statement (5) is correct

Since the other 4 statements are incorrect, then it must be statement (5) is correct . Thus $\boxed{5}$ is the answer.

Since it is clearly given that only one statement is correct, statements 1 and 4 are of course wrong.

Now, if statement 3 is correct, statement 2 also has to be correct as statement 1 is wrong

That again violates the given condition and hence statement 3 is wrong

But if statement 3 is false, it means statement 2 is also false

The only statement left is statement 5 and it is correct

Because the other answer just make another answer right, choose the one that make another answer is wrong. So, the answer is 5!

Using proof of contradiction we consider the conclusion/last statement to be true and as a propositional statement, we can see a contradiction between the statements so we can conclude that statement 5 is true.

5 is right but i don't like it being right because it is grammatically incorrect

i just got it

just read the statements carefully, and you will find that all statements contradicts each other leaving the statement 5

Only one statement is correct..

then, (1) and (4) is wrong

check (3), if (3) correct, then (2) correct, because (1) is wrong, but if both (2) and (3) correct, it contradict each other

then none of (1) (2) (3) (4) is correct

statement (5) is correct

5

if we see the right instructions of every statement [except last statement ] we can't find any statement right. in last we read statement that None of the statements above is correct. then it is right .

1 is correct 2 is correct id 2 is correct 1 is wrong so 1 and 2 are wrong if both are wrong 3 is wrong if 3 is wrong 4 is also wrong so 5 is correct

I don't know, why problem setter fixed this kind of problem category is Combinations! In this problem we don't have any statement. So we can't compare any of statement, so we sure that statement number 5 is correct

The 5th answers correct

Let's go through each statement one by one. The first one says that every statement below is correct. But , the third statement says only one of the statements above is correct, so that means statement one is incorrect. If the first statement is incorrect, that means the fourth statement is also incorrect because it says every statement above is correct. The second statement is wrong, because we know that the first statement is incorrect, so one of the statements below statement two has to be correct. The third statement is wrong because it says only one of the statements above is correct, but both of them aren't. That leaves statement 5 to be the correct answer. The correct answer is 5.