Mathematica commands needed to solve problem in Set Theory!

• To: mathgroup at smc.vnet.net
• Subject: [mg43610] Mathematica commands needed to solve problem in Set Theory!
• From: gilmar.rodriguez at nwfwmd.state.fl.us (Gilmar Rodríguez Pierluissi)
• Date: Tue, 23 Sep 2003 04:02:03 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```The following is a problem from Set Theory, that I have

attempted to solve using the standard, Mathematica Set

Theoretic tools (i.e. Union, Intersection, and Complement)

with no success.

Here is the problem:

************************************************************

Johnny (an assumed name to protect the inocent) is looking

for his ideal girfriend, which according to his predilections,

must be red-haired, green-eyed, slender, and tall.

He knows four women: Adele, Betty, Carol, and Doris.

Here are the requirements that they meet:

0. Only one of the four women has all four characteristics

that Johnny requires.

1. Only three of the women are both green-eyed and slender.

2. Only two of the women are both red-haired and tall.

3. Only two of the women are both slender and tall.

4. Only one of the women is both green-eyed and red haired.

5. Adele and Betty have the same color eyes.

6. Betty and Carol have the same color hair.

7. Carol and Doris have different builds.

8. Doris and Adele are the same height.

Which one of the four women satisfies all of Johnny's

requirements?

************************************************************

Your assistance in solving this problem(using Mathematica

commands) will be greatly appreciated!

```

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