Re: Logical Implication and Equivalence
- From: herbzet <herbzet@xxxxxxxxx>
- Date: Tue, 28 Nov 2006 20:49:58 -0500
Mad_man_on_a_MissIon wrote:
Will someone please explain to me how you are supposed to use logical
implication and/or equivalence to solve this.....
Bill, Sue, and Alice are lined up facing forward with Bill first, then
Sue, then Alice. From a collection that they know contains 3 blue and 2
red hats. Hats are placed on their heads while they are blindfolded.
The Blind folds are removed, but they continue to face forward and see
only the hats in front of them. Bill sees none, Sue sees Bill's, Alice
sees both Sue and Bill's. Alice claims she does not know what color her
hat is. Sue also claims she does not know what color her hat is. Now
Bill knows what color his hat is. What is it?
I'll have a go at it:
If Bill and Sue both had red hats, Alice would know that she is
wearing a blue hat, because there are only two red hats. But
she does not know that she is wearing a blue hat, therefore Bill
and Sue are not both wearing red hats.
Bill and Sue are either both wearing blue hats, or one of them
is wearing a blue hat and one is wearing a red hat.
Sue, realizing this, concludes that if Bill is wearing a red hat,
then she must be wearing a blue hat. But she does not know that
she is wearing a blue hat, therefore Bill is not wearing a red hat.
Therefore, Bill is wearing a blue hat.
Bill, realizing all this, concludes that he is wearing a blue hat.
--
hz
.
- References:
- Logical Implication and Equivalence
- From: Mad_man_on_a_MissIon
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