Everyone is pointing towards the other one

There are 4 cases:

Because all but the third case reveals a contradiction, then the only possible scenario is the third case, with statement B being false.

Case 1: A is false implies D is false (since A says D is true). Therefore, we have 2 false statements. So, this case is rejected.

Case 2: B is false implies A is true (since B says A is false). A is true implies D is true, which implies C is true, which implies B is false. Therefore, the case in which B is false is consistent.

Case 3: C is false implies B is true (since C says B is false). B is true implies A is false. So, we have two false statements. Therefore, this case is rejected.

Case 4: D is false implies C is false (since D says C is true). So, we have two false statements. So, case 4 is rejected.

The case in which B is false (case 2) is the only one which is consistent with the claim that there is only one false statement. Therefore, B is the false statement.

When Statement B is true, it results in Statement A being false, which results in being Statement D also false. This results in more than one false statement.

Hence Statement B itself is False.

Assume that Statement A is true $\Rightarrow$ Statement D is true $\Rightarrow$ Statement C is true $\Rightarrow$ Statement B is false . Cheers!

If A is false, D is false. Since that cannot be (assuming that the statement in the question is true) A and D are both true. Therefore C is true. This implies that B is false.

Only statement B and C say "Statement ... is false "

Therefore, one of them must be false, because otherwise we would have two false statements.

If B is false: A is true -> D is true -> C is true

If C is false: B is true -> A is false -> D is false

So only if B is false, we have exactly one false answer. Therefore B is the false answer.

There are four possibilities: either A, B, C, or D are false. We know right away that A and D cannot be false since their being false makes their target statement false also. Out of B and C we need one that results in their target statement being false and the target's target being false. Only B satisfies this.

I got lucky by testing A as true first lol

If C is telling the truth, the B is false and D is true. Then C will be true and will say that B is false.

In the case that A is false, then D must also be. Since there is only one false statement, A must be true. Assuming that A is true, then D is also true. D states that C is true, and C states that be is false. Therefore, B is false.

Another way to look at this is to consider each case separately.

-If A is false, then D is, so A is true. -If B is false, then it makes sense, but if it's true, then we have three false statements (A, D, C) -If C is false, then statement B is true, making A false, which makes D false, so we again have three false statements. -If D is false, then C is is also false, making B true. This means that A is true. Now we have two false statements (C, D).

Now we've done it in two different ways, each with the same result: B is false.

Becomes much too easy when you realize that two of the statements (B and C) claim 2 different statements among them to be false, when there should be only one statement as false. This leads us: One of those (B and C) accusations has to be false. Since there only is one statement false, the other one will then have to be correct.

If C was false (and therefore B was correct), then (as required by B) A would also have to be false along with the C; which inevitably requires B to be false. B being false also happens to be the claim of C, which leaves us paradox-free.

Lets pick a statement to start with, and see where we have any issues. Say, Statement A.

Lets say A is true If A is true, then D is true.

If D is true then C is true

If C is true then B is false

If B is false then A is true. (B claims A is false)

A, D, C, all true, only if B is false.

Assuming there is only one solution, we found it! B is false! but lets double check. Lets try to prove that it is the only solution.

Lets say B is true. (After all, B is either true, or false. Is there a situation B could be true and still follow the rules?) If B is true, then A is false. If A is false then D is false. (A claims D is true) - Oops! there is only one false statement, this is wrong. This means B MUST be false.

At this point we know that in order to have only one false statement, B must be that false statement. Proof by contradiction. Q. E. D.

Note that if we had started with any of the statements (other than B) we would have arrived at the same "solution" Lets say C is true We already know this will turn out the same as we first found. B is false, A is true, etc.

If D is true? C is true, B is False, A is True, etc.

The only time we get a contradiction is if we say B is true.

If A is False, then D must also be False. But that leaves two False statements, which is against the rule. If D is False, then C must also be False. Again, against the rule. If C is False, then D is also False. That leaves statement B to be the lie.

If A is true, then D is true. If D is true, C is also true. Assuming C is true, B is false. If B is false, then A is true, which is where we started.

you just start by checking if statement A is false then the other 3 statements have to be true, that they are not, so luckily for me I did the same thing for statement B and eventually every other statement is true, so its statement B the one that is false. No need to check next cases since it has to be only one that states

Statement B is false because if it's true, everything else is false.

Statement A tells us that statement D is true, which led me to statement D, which tells us that C is correct. Then it says that statement C states that statement B is false, but statement B says that statement A is false. If what statement B says is true, then that would mean that there are several false statements, those being statements A, C, and D. My conclusion, statement B is the only false statement.

I start from the statement A, I assume that the statement is true, then there will be two others statement must be true (from the condition that only one statement is false). When A is true then D is true and C is true. it means B is false, so A is not false as what I assume before. So and this can fulfill the condition.

Answer choice $B$ contains the only statement that, when asserted true would imply that more than one of the answer choices (all others $A$ , $C$ , and $D$ except $B$ itself) would contain false statements. The problem states that only one answer choice contains a false statement. Asserting each of the other answer choices $A$ , $C$ , or $D$ individually each implies that only $B$ contains a false statement.

Thus, we identify the only statement among the answer choices that must be false among the other statements. Answer choice $B$ contains the correct answer to the problem statement that asks to identify the answer choice that contains a false statement (where all the answer choices contain possibly true statements, and only one among them is false).

This problem seems "difficult" at first because one might not readily recognize the difference between "the validity of asserting an answer choice" and "the truth of a given statement (contained within an answer choice)".

Finally, asserting the negation of the statement in $B$ leads to a contradiction that the original statement in $B$ is true. However, each of the other statements are tautological when negated: asserting the negation of any other statement $A$ , $C$ , or $D$ implies precisely the negation of $A$ , $C$ , or $D$ respectively. All implications in each of the assertions above are consistent with the problem statement except for the contradiction raised by $\neg B$ . Therefore, answer choice $B$ contains the only false statement about the other answer choices (which are themselves, recursively, statements about the other choices in the closed set of choices).

Odds are good that any one statement is true. Let's assume A is true. Then D is true. Then C is true, and B is false. B claims A is false, which is false. Hence, B really is false.

It's one thing to prove that only B can be false, it's another to pick the correct answer. See Nihar and challenge by Challenge Master above.

This is just another test. Yes, that "have a challenge master read" feature disappears once an answer is posted.