Guilty or Innocent? (Pt. 2)

Logic Level 2

Let's say that you are witnessing another trial, this time involving four people (A, B, C, and D).

These four facts were shown:

  1. If A is guilty, then B was an accomplice

  2. If B is guilty, then C was an accomplice or A is innocent

  3. If D is innocent, then A is guilty and C is innocent

  4. If D is guilty, A is guilty

The jury's results were inconclusive, so they turn to you for help.

Are any of them able to be found guilty or innocent?

They are all guilty B is guilty C is guilty A is guilty D is guilty

Rajam Arunprakash by Rajam Arunprakash , 14, USA

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2 solutions

Saya Suka
Apr 13, 2021

By 3 & 4, no matter the state of D, A must be guilty. By 1, B is an accomplice and also guilty. By 2, C must be another accomplice and also guilty. By the guilt of the 3 of them (A, B and C), D must be the last guilty person.

Btw, #1, #2 & #4 use the true form of "If [true], then [true]", while #3 uses the true form of "If [false], then [false]".

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Here is my reasoning:

By 3, if D is innocent, then A is guilty. However, by 4, if D is guilty, then A is guilty!

  • This means that regardless of whether D is innocent or guilty, A must be guilty.

  • Now that A is proven to be guilty, B can also be found as guilty because of 1.

  • Then by 2, C is an accomplice or A is innocent. A has already been proven to be guilty, which means C is an accomplice as well.

  • Finally, by 3, if D is innocent, then A is guilty and C is innocent. C isn't innocent, so D is not innocent!

Therefore, all of them are guilty.

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