Simple yet confusing

If 1) were true then both 1) and 2) would be true, which can't be the case since only one statement is true.

Therefore 1) must be false and so 2) must be false. 2) says 5) is false, but since 2) is false, 5) is true.

Remark: Clearly 3 and 4 are both false since they make claims contradictory to the given that exactly one statement is true.

if statement 1 was true that it would mean that (2) is also true which is not possible since only 1 statement can be true

if (2) is correct it would imply that (1) is also true ,again a fallacy

all the five statements can't be true and neither can all the five be false

hence (5) must be the answer!

I did it right but that is logically not right , the question said that only one statement is correct . Statement 5 says that statement 1 is false and that means that statement 2 is false so that means that statement 5 is true which means that statement 2 is also correct .

3) is absolutely false since the question states that "Only one of the following statements is true". While 3) states that All statements (1,2,3,4,5) are true contradicts what the question states. 4) is also absolutely false since: a. The question contradicts the statements b. If 4) are true, it will contradict since 4) states that (1,2,3,4,5) are all false, while 4 is true, the statement says that it is false

Then, analyse statement 1, 2 or 5. Case 1: 1) is true If 1) is true, then 2) must be true. Automatically, 5) must be false. Here, we have that 1) and 2) are true, so it contradicts the question Case 2: 1) is false If 1) is false, then 2) must be false. Automatically, 5) is true. Thus, there is no contradiction between the number's statements and there will be only one of the following statements is true. So the answer must be 5)

1 can't be true, since if it were true, so would statement 2 be, which contradicts the conditions of the question. 2 can't be true, since it states 5 is false, making 1 true, and that also is a contradiction. 3 and 4 are automatically false since they each contradict the condition that only one statement is true. Therefore 5 is the answer.

After reading all the statements the results are like this: but since statement 1 implies that statement 2 is true, statement 2 is already false and it can't be true because statement 2 implies that statement 5 is false when it is true so statement 5 is true.

If statement 1 is true, than statement 2 is true, leading to 2 true statements, which is not possible. So statement 1 is necessarily false.

If statement 5 is false, so statement 1 is true, but statement 1 is necessarily false, so statement 5 is not false and must be true.

Since only one true statement is possible, it must be statement 5.

Initial information is that one statement is true. Therefore 3 and 4 are false and we only consider 1 2 and 5.

I used systematic casework to solve the problem, assuming one is true and the others are false. The way I did it is by keeping track of 2 variables, whether a statement is true or not, and what information it "points" towards another statement. If a statement is true, it must point a false towards a false statement or a true towards a true statement, and vice versa if the statement is false. Because there is only one true statement, 1 is out because it has a true pointer. If 2 is true, it points a false towards 5 which then points a true towards 1, so 2 is out because there is only one true. That leaves 5 because 5 points a false towards a true, which causes it to point a false towards a 2, which points a true at 5 leaving only 1 true.

Sorry if this was a bad explanation, its my first time solution writing...