Math Is Fun Forum

Median Joe

Member

Registered: 2019-12-04

Posts: 9

Logic Puzzle

This puzzle is from the book "Boolean Algebra and its Applications" by J. Eldon Whitesitt, but there is no solution given, so I'm interested in what anyone proposes. I tried 3 major AI platforms (Google Gemini, claude.ai and ChatGPT) and only ChatGPT came up with the answer which matched mine.

Here is the problem:

Simplify to a single rule the following set of rules regarding dress to be worn to a certain party for married couples:

1. If a man wears either a tie or a coat, then his wife must wear neither high heels nor a hat.

2. If a woman wears slacks or a hat, then her husband must wear either a tie or a hat, but not both.

3. No man and wife may both wear hats unless either the wife wears high heels and slacks or the man wears a tie and does not wear a coat.

4. For every couple, either the man or his wife must wear a hat and either the man wears a coat and the wife wears slacks.

5. If a man wears a hat or his wife wears slacks, then the man must wear a tie and his wife must not wear high heels.