From these nine statements, what, if anything, can we conclude about the connection between seeing a...

logic/mermaids New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

From these nine statements, what, if anything, can we conclude about
the connection between seeing a mermaid and having a hangover?

1. Everyone who believes that mermaids exist has visited Atlantis.

2. Only people who have found favor with the gods are protected by
   Neptune.

3. No one who has not tasted real ambrosia has partaken of food with
   the gods.

4. People who do not believe that mermaids exist have never seen a
   mermaid.

5. Everyone who has tasted real ambrosia has a hangover.

6. Only people who have partaken of food with the gods have ever been
   invited to Mount Olympus.

7. No one who has not survived a shipwreck has visited Atlantis.

8. Everyone who has found favor with the gods has been invited to
   Mount Olympus.

9. No one who is not protected by Neptune has survived a shipwreck.

-- <warthog@ccnet.com>, "Mermaids and hangovers", September 1995

[ Editor: the numbering is Matthew Blum's, from his reply. ]

Show solution

We can conclude that, if you have seen a mermaid, then you have a
hangover.

For purposes of explanation, I've numbered the clauses.

Suppose you have seen a mermaid.  By 4, you must believe mermaids
exist.  So, by 1, you must have visited Atlantis.  So, by 7, you must
have survived a shipwreck.  So, by 9, you must be protected by Neptune.
So, by 2, you must have found favor with the gods.  So, by 8, you must
have been invited to Mt. Olympus.  So, by 6, you must have partaken of
food with the gods.  So, by 3, you must have tasted real ambrosia.  So,
by 5, you must have a hangover.

-- Matthew A Blum <mblum@world.std.com>