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This is a classic from Lewis Carroll. Suppose we are given that

  • Babies are illogical;
  • Nobody is despised who can manage a crocodile;
  • Illogical persons are despised.
What conclusion can we draw that uses all three of these premises?
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Me in a rare cheerful mood

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Babies can't manage crocodiles?  Sorry, I think my computing logic is spoiling this gag.


Does this help?
My wife sent me to the shops for "A loaf of bread and if they have eggs, get six".
I went home with six loaves of bread.  She was cross and asked why.  I said "Because they had eggs".

Richard Walker

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Agreed about the babies and crocs, but the question was really how to explain the reasoning that leads to the conclusion. 😊

Me in a rare cheerful mood

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Sorry.

Using algebra, where B = babies, I = illogical persons, D = despised, M = can manage a crocodile.

We are told:
B = I
No D = M, so D <> M  (not quite right, I should have used sets rather than algebra here).
I = D

As B = I and I = D then B = D.

Since D <> M and B = D then B <> M.

So, babies are not those who can manage crocodiles.

That required use of the third premise, although it does not use it explicitly.


As an aside:

Despicable, illogical, babies you see
For incompetent crocodile wranglers they be.

Or, we can conclude people prefer crocodile wranglers to babies.


Or, using sets, where:
I is the set of all illogical persons.
B is all baby persons.
P is all illogical persons
W is all crocodile wranglers
D is the set of all things despised.

B is a member of I.
I is a member of D.
So B is a member of D.

We are told no member of set D is a member of set W.

So B cannot be a member of W.  So Babies cannot manage crocodiles.


I cannot see any other logically correct conclusions that use all three premises.

Me in a rare cheerful mood

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How about a truth table (which is taking me back to being a programmer in the 1980s:



Illogical Despised Manage crocodiles
Babies Y Y N
Despised people N/k - N
Illogical people - Y N

Illogical persons cannot manage crocodiles (two premises).

Babies are despised (two premises).

Babies can't manage crocodiles (three premises).


Me in a rare cheerful mood

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Babies, as civilians,

Have logic diabolical.

Wranglers of crocodilians

Have friendships psychological.

Socialisers most chronical

Are thinkers quite not logical.

So babies diabolical are cared for oh so chronical,
so cannot be mythological zoological reptilian
wranglers or stranglers or managers idealogical.


That's my lot.  I'm done here.  smile

Richard Walker

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I'm going to try Venn diagrams in the morning.

smile

Richard Walker

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I was thinking of Venn diagram.

The premises given tell us the situation is as below, and no babies are crocodile handlers or vice versa.


Me in a rare cheerful mood

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You went and did one!  I thought you were kidding.

I was going to and found my LibreOffice Draw crashes on loading and after a while faffing discovered it was caused by an extension I installed a few years ago that no longer works.  So that amused me yesterday and today.

Me in a rare cheerful mood

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Also in Viz, and cleaned up slightly:

Next door's dog keeps pooing in our garden so my wife said "Next time it does that, get a shovel and throw it over the fence".  So I did and now she's furious.  There's still dog poo in our garden and the neighbours have our shovel.