This Statement is False. Wait What?

Logic Level 1

Out of the 8 statements below, how many of them is/are true?

(A) Statement B is false.
(B) Statement C is false.
(C) Statement D is false.
(D) Statement E is false.
(E) Statement F is false.
(F) Statement G is false.
(G) Statement H is false.
(H) Statement A is false.

3 1 4 2 5

2 solutions

Chew-Seong Cheong
Oct 5, 2015

Statement A can either be $\color{#3D99F6}{T}$ rue or $\color{#D61F06}{F}$ alse. The following is the truth table for if both statement A is $\color{#3D99F6}{T}$ rue and statement A is $\color{#D61F06}{F}$ alse.

$\begin{array} {rll} \text{If A is } & \color{#3D99F6}{T} & \color{#D61F06}{F} \\ \text{then B is } & \color{#D61F06}{F} & \color{#3D99F6}{T} \\ \text{then C is } & \color{#3D99F6}{T} & \color{#D61F06}{F} \\ \text{then D is } & \color{#D61F06}{F} & \color{#3D99F6}{T} \\ \text{then E is } & \color{#3D99F6}{T} & \color{#D61F06}{F} \\ \text{then F is } & \color{#D61F06}{F} & \color{#3D99F6}{T} \\ \text{then G is } & \color{#3D99F6}{T} & \color{#D61F06}{F} \\ \text{then H is } & \color{#D61F06}{F} & \color{#3D99F6}{T} \end{array}$

We see that in both cases the number of true statements is $\boxed{4}$ . We note that the statements are cyclical and we will get the same result if we have started with statement other than A.

Interesting result. What might have happened if the problem read like this instead?

A) Statement B is false.
B) Statement C is false.
$\hspace{1.5cm} \vdots$
H) Statement I is false.
I) Statement A is false.

Basically, what happens if we have a cycle of 9 statements like this, rather than 8?

Andrew Ellinor - 5 years, 8 months ago

Then we will have a paradox, since if A is true, then it implies that B is false, then C is true, D is false, ..., I is true meaning that A is false, but that causes A to be true and false at the same time.

On the other hand, if A is false, then B is true, C is false, D is true, ..., I is false meaning that A is true, which also causes A to be true and false at the same time.

In general, if the number of statements is odd then we will have a paradox.

Kenneth Tan - 5 years, 8 months ago

Excellent!

Andrew Ellinor - 5 years, 8 months ago

Not a tough one... I did the same way..

Bhupendra Jangir - 5 years, 8 months ago

Well I still can't get the solution you people are trying to say.

Mythreyi Venkataraman - 5 years, 7 months ago

Phan Hà Anh
Jan 10, 2016

Let's imagine that Statement A is True ( You can say that it's False. Whatever ) If A is : T or F B is : F or T C is : T or F And go on.......... Until H is F or T Then you count it............it's 4 !

This Statement is False. Wait What?

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