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Tuesday, December 20, 2005

Scribe or what ?


Well we started off today with some questions on the board :
1) One of the Isle of view (say it aloud =P) knights always tell the truth and knaves always lie. You just arrived and met two people, Mr. A and Mr. B. Mr. A says, "At least one of us is a knave" . What are A and B ?

First make the assumption that the speaker (Mr. A) is one or the other. We'll pretend that Mr. A is a knave, meaning he only lies. If he was a knave and he said that he'd be speaking the truth and he can't do that. They both can't be knaves because then the statement would be a true statement. If we had one knave and one knight, the statement would be true, therefore Mr. A can't be a knave and he has to be a knight.

Mr. A = knight
Mr. B = knave

* Proof by contradiction
- assume the opposite
- if there is a contradiction, then the opposite must be true

2) A little later you meet Ms. C and Ms. D. Ms. C says "I'm a knave but D isn't." What are C and D?

C can't be a knight because she can't say she's a knave because that would be a lie. Therefore she has to be a knave. (indirect)
Assume : Ms. C is a knave (liar)
In logical a conjuction both ideas have to be true for the statement to be true. However, if one idea or part of the conjuction is false then the whole thing is false.

Ms C is knave meaning that she can't say that she's a knave .. BUT when she used a conjuction and put together a true AND a false statement .. meaning that she lied .

Ms. C is knave meaning that Ms. D must also be a knave because the second part of her conjuction has to be false "but D isn't" meaning the opposite.


Next we got a hand out called "
Matrix Logic Problems". We did that first one in class.

1) Three of our Olympic swimmers took 1st, 2nd, and 3rd in their race at the Olympic games. When they went to the victory stand each wore a different colored swimsuit. From the clues below tell the name, place, and swimsuit color of each swimmer.

a) The first place swimmer wore a
red swimsuit.
b) Tract took 3rd place.
c) Nancy wore
blue.
d) Mary and the girl in the white swimsuit were roommates.

Using the clues above and using a matrix, we get this :
Now using some thinking ..We get that Mary must be red because she can't be white or blue, and she has to be 1st because 1st place wears red. Nancy wears blue (given), which means that the only color that Tracy can wear is white. Also Tracy is 3rd (given) meaning that 3rd place winners wear white. Then the only place left is 2nd, and Nancy is the only one left and she wears blue.

Meaning:
Mary - 1st - Red
Nancy - 2nd - Blue
Tracy - 3rd - White


Also we got a story called "A usual day at Unusual School" BUT .. I won't give you my answers because it's due tomorrow and it's more fun figuring things out on your own =)


1 Comments:

At 12/20/2005 7:50 PM, Blogger AichelleS. said...

nice haha I like it gooood job

 

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