CS1FC3-slides-2012-02-01_2up_letter

# CS1FC3-slides-2012-02-01_2up_letter - Ladies or Tigers...

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Unformatted text preview: Ladies or Tigers: First and Third Cases (Ex. 3.9) In the first case, the following signs are on the doors of the rooms: 1 In this room there is a lady, and in the other room there is a tiger. 2 In one of these rooms there is a lady, and in one of these rooms there is a tiger. We are told that one of the signs is true, and the other one is false. In the third case, the following signs are on the doors of the rooms: 1 Either a tiger is in this room or a lady is in the other room 2 A lady is in the other room We are told that the signs are either both true or both false. Mathematics for Computing COMP SCI 1FC3 McMaster University, Winter 2012 Wolfram Kahl [email protected] 1 February 2012 Plan for Today Textbook Chapter 3: Propositional Calculus Conjunction Doing proofs Ladies or Tigers: Third Case 1 Either a tiger is in this room or a lady is in the other room 2 A lady is in the other room We are told that the signs are either both true or both false. R 1 L : There is a lady in room 1 R 2 L : There is a lady in room 2 S 1 ≡ ¬ R 1 L negationslash≡ R 2 L S 2 ≡ R 1 L S 1 ≡ S 2 Ladies or Tigers: Third Case 1 Either a tiger is in this room or a lady is in the other room 2 A lady is in the other room We are told that the signs are either both true or both false. R 1 L : There is a lady in room 1 R 2 L : There is a lady in room 2 S 1 ≡ ¬ R 1 L negationslash≡ R 2 L S 2 ≡ R 1 L S 1 ≡ S 2 = ( Def. S 1 , S 2 ) ( ¬ R 1 L negationslash≡ R 2 L ) ≡ R 1 L = ( (3.14) ( p negationslash≡ q ) ≡ ¬ p ≡ q ) ¬¬ R 1 L ≡ R 2...
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