Regarding the same logic riddle as before

[fleet fossil]

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[fleet fossil]

@crude anvil

[crude anvil]

so did you find out which one is false?

[fleet fossil]

How do I quickly find out if there is a contradiction or not?

Is there a structured way?

It wouldn't be that hard to miss one

[crude anvil]

age is a linear order

if there are no contradictions you must be able to form a chain

[fleet fossil]

The problem is with these multiple people after >

[crude anvil]

you are thinking about it correctly based on your last topic

[fleet fossil]

A > E, D > but now everything is messed up because I need two new chains in parallel

[crude anvil]

there is only one chain

contradictions in this chain are always of the form X>Y>X

[fleet fossil]

(1) A > E

(2) C > B

(3) A > D

(4) E > C

(5) C > A

(6) E > D

(7) D > C

Now assume the first is false

So A <= E

now uh

[crude anvil]

2-7 must be true then

[fleet fossil]

C > B > uh

[crude anvil]

A>D>C>A

contradiction

[fleet fossil]

oh

Ok assume C <= B now

A > E > C > A

Assume A <= D now

A > E > C > A

Assume E <= C now

A > E > D > C > B

Everything looks fine?

[fleet fossil]

So is this it?

(4) is false

[fleet fossil]

'Show it is unique'

So we need to play it through for the other cases too?

[crude anvil]

that's not what I got

[fleet fossil]

oh wait

[fleet fossil]

This contradictss E <= C

[crude anvil]

if 4 is false then A>E>D>C>A

no good

[fleet fossil]

Assume C <= A

A > E > D > C > B

Is C <= A also fulfilled? Yes!

So everything is fine

(5) is false

[fleet fossil]

Is this what you got?

[crude anvil]

correct

[fleet fossil]

Ok now we still need to show uniqueness

So go through (6) and (7) too?

[crude anvil]

uniqueness of what

[fleet fossil]

Assume E <= D

[crude anvil]

the ordering?

[spiral flame]

You don't need to check statements that don't resolve the contradiction.

[fleet fossil]

"show it is unique"

[crude anvil]

the ordering

[fleet fossil]

yeah

[spiral flame]

The contradiction is caused by a > e, e > c, a < c.

[fleet fossil]

Ah

Thank you all!

[spiral flame]

Because of the transitivity of greater than.

[fleet fossil]

Thanks @crude anvil , @spiral flame

[humble lodge]

@fleet fossil has given 1 rep to @spiral flame @crude anvil

[fleet fossil]

+close