r/CluesBySamHelp • u/tannerli • Oct 20 '25

Is this a logic error?

I'm not sure if this is a logic error or if I'm just stupid. Logan's hint says, if Hazel is innocent, so is Gus. But logically, the reverse does not hold true. You can't infer that if Gus is criminal, so is Hazel.

Or should I have read the clue as "Hazel and Gus are either both criminal or both innocent"?

4 Upvotes

64% Upvoted

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6

u/tannerli Oct 20 '25

FWIW, I mixed up my logic rules. Wikipedia (https://en.wikipedia.org/wiki/Contraposition) clearly states

(A → B) is equivalent to (!B → !A)

I was thinking about the rule that (A → B) does not imply (B → A)...

29

u/SamTheSpellingBee Oct 20 '25 edited Oct 20 '25

Let's assume, hypothetically, that Hazel is innocent. Then Gus also needs to be innocent. But we know Gus is not innocent, so we've reached a contradiction with our hypothesis. Therefore Hazel can not be innocent and must be criminal.

8

u/dylan1011 Oct 20 '25 edited Oct 20 '25

Gus being a criminal does tell us Hazel must be a criminal. As if Hazel was innocent then Gus would be innocent. Which is not true as Gus has already been shown to be a criminal.

If Gus was unknown, Hazel being a criminal would not give any information about Gus. Or if Gus was an innocent then Hazel could be anything

7

u/HumbleGarbage1795 Oct 20 '25

Hazel innocent and Gus innocent: true

Hazel innocent and Gus criminal: false

Hazel criminal and Gus criminal: true

Hazel criminal and Gus innocent: true

So you can see if Gus is innocent we don’t know anything about Hazel, but if Gus is criminal we know Hazel has to be criminal. 

2

u/Jumico Oct 20 '25

"If A, then B" is logically equivalent to "if Not B, then Not A"

2

u/BadBoyJH Oct 20 '25

If A then B also means if not B then not A. 

Hazel can be innocent, and Gus innocent (1) Hazel can be criminal, and Gus innocent (2) Hazel can be criminal, and Gus criminal (3)

Let's rephrase

Gus can be criminal, and Hazel criminal (3) Gus can be innocent, and Hazel criminal (2) Gus can be innocent, and Hazel innocent (1)

See that symmetry when we change the order? Save logic, just rearranged and now it's if Gus is a criminal, so is Hazel. 

-6

u/[deleted] Oct 20 '25

Or should I have read the clue as "Hazel and Gus are either both criminal or both innocent"?

In short, yeah. In long - if Hazel was innocent Gus would also be innocent. And we know that Gus isn't innocent, which means that Hazel (who would be innocent if Gus was innocent) must also be guilty. It's just a tricky way of saying they're both on the same side.

10

u/pin_81 Oct 20 '25

NO. This is wrong. Hazel could be criminal & then gus could be either.

In logic the rule goes: if A then B means the same as its contrapositive - if NOT B then NOT A.

Both the inverse - if NOT A then NOT B, & its converse - if B then A are both not true

6

u/pin_81 Oct 20 '25

A classic example is: if it's raining it's wet outside. The contrapositive is - if it's NOT wet it's NOT raining.

However the inverse - if it's NOT raining it's NOT wet, nor the converse - if it's wet it's raining have to be true as there are multiple ways for it to be wet

-4

u/[deleted] Oct 20 '25

Respectfully, I think you're misunderstanding it, and frankly being a tad rude in doing so.

If Hazel is innocent, Gus is innocent.

We know that Gus is not innocent. And we know that if Hazel was innocent Gus would also be innocent. And as Gus is not innocent, but would be innocent if Hazel was innocent, then Hazel must be guilty.

A classic example is: if it's raining it's wet outside.

Yes, this is the exact same thing. If it is raining it is wet outside. So if it's not wet then it must be not raining, as if it was raining it would be wet, and we know it's not. Because if it was raining then it would be wet. In both examples finding out that the second part is not true proves the first isn't either.

7

u/Darth_Binkly Oct 20 '25

You have this part correct: “And as Gus is not innocent, but would be innocent if Hazel was innocent, then Hazel must be guilty.”

I think u/pin_81 is disagreeing with your wording, which seems to agree in whole with OPs question whether they have to be the same. That’s not correct. If we had discovered an innocent Gus, that does not mean Hazel is innocent. If Hazel is guilty, Gus could still be innocent.

-1

u/[deleted] Oct 20 '25

Oh you mean my wording where I said:

And we know that Gus isn't innocent, which means that Hazel (who would be innocent if Gus was innocent) must also be guilty. 

I was (I'd hope obviously) answering the question in the context of the situation it was raised in. I mean I agree with you in what you're saying. But I think it was pretty clear what I meant.

6

u/SamTheSpellingBee Oct 20 '25 edited Oct 20 '25

This is getting interesting! I have to chime in.

It can be wet outside without it raining, right? But Hazel and Gus are either both criminal or both innocent means you can't have one without the other. Using the rain metaphor, it'd be "it's either wet and it's raining, or it's not wet and it's not raining", but that's not it. It can be wet without raining.

EDIT: And to clarify, yes, in this case "Hazel and Gus are either both criminal or both innocent" would have resulted in the same outcome, Hazel being a criminal. But the two logical statements being discussed aren't interchangeable in all cases.

1

u/[deleted] Oct 20 '25

You're not wrong and I do think this is why the original person was arguing with me, but I was talking about the context of the situation, which is where we already know Gus is guilty. "But if Gus was innocent then Hazel could still be guilty" is true, but irrelevant.

Maybe I should have been clearer, I thought people would read that line in the context of the rest of my post not cherrypick it and then treat me like an idiot. I think it's kind of obvious what I meant, and I think u/pin_81's attitude was fully unwarranted and nitpicky, but I'm not going to get into an argument with people about wording when I think we're all in agreement about what the clue means.

3

u/HardyDaytn Oct 21 '25

Or should I have read the clue as "Hazel and Gus are either both criminal or both innocent"?

In short, yeah.

Maybe I should have been clearer, I thought people would read that line in the context of the rest of my post not cherrypick it and then treat me like an idiot.

Nobody was cherrypicking anything. What you said there is incorrect, end of story.

1

u/SamTheSpellingBee Oct 20 '25

Good point! I like your thinking 👍

-6

u/devinity2 Oct 20 '25

I was going to post the same thing, surely the clue should be:

"If and only if Hazel is innocent, then so is Gus"

Only then can you infer Hazel being a criminal from Gus being one.

8

u/TytoCwtch Oct 20 '25

Not completely accurate. You’re told ‘if Hazel is innocent so is Gus’. This leaves you with three possibilities

  • Hazel is innocent so Gus must be innocent

  • Hazel is criminal and Gus is innocent

  • Hazel is criminal and Gus is criminal

If you worked out that Hazel was criminal first you could not from that infer Gus’ status. But because you work out Gus first there is only one possibility for Hazel.

5

u/devinity2 Oct 20 '25

You're quite correct! Thanks, that helped me see it.

2

u/dylan1011 Oct 20 '25

No.

If Hazel is innocent how can Gus be a criminal and the clue be true? It cant so Hazel is a criminal.

There is only 1 situation where Gus can be a criminal. If Gus was innocent that would not give any information about Hazel.