Guilty or Innocent?

Logic Level 2

This question involves a particular trial of three people, A, B, and C for involvement in a crime.

In this case, two facts were able to be found.

  1. If A is innocent or B is guilty, then C is guilty.

  2. If A is innocent, then C is innocent.

Can any of the three be found guilty?

Yes. Only A No. Yes. Only C Yes. Only B

Rajam Arunprakash by Rajam Arunprakash , 14, USA

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2 solutions

The approach to this problem is simple:

  • By 1, if A is innocent then C is guilty.

  • However, by 2, if A is innocent, then C is innocent.

  • This implies that C is both guilty and innocent at the same time which is impossible.

  • So A cannot be innocent, so A is guilty.

The guilt for either B or C cannot be established with the given facts.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Saya Suka
Apr 3, 2021

The two then part of the statements are contradictory even though both are the true facts, so one of them must be true in one way (false if and false then) and the other is true in another way (true then and whatever ifs).

That means that at least one of the antecedents (or if parts of the statements) must be false, but an innocent A will make both ifs true, so A must be guilty.

Additionally, B and C can be either guilty or innocent, but the two would be in it together.

In conclusion, either A is guilty alone or they are all guilty, but A is guilty one way or another.

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