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Unformatted text preview: getting wrong right Be careful proving a claim false. Consider the claim, for some suitably de ned X; Y and P; Q : S : 8 x 2 X; 8 y 2 Y; P ( x; y ) ) Q ( x; y ) To disprove S , should you prove: 8 x 2 X; 8 y 2 Y; P ( x; y ) ) : Q ( x; y ) What about 8 x 2 X; 8 y 2 Y; : ( P ( x; y ) ) Q ( x; y )) Explain why, or why not. slide 5 pop quiz De ne T ( n ) by: 8 n 2 N T ( n ) , 9 i 2 N ; n = 7 i + 1 : Take some scrap paper, don't write your name on it, and ll in as much of the proof of the following claim as possible: 8 n 2 N ; T ( n ) ) T ( n 2 ) Now ll in as much of the disproof of the following claim as possible: 8 n 2 N ; T ( n 2 ) ) T ( n ) slide 6 allowed inference At this point you've been introduced to some rules of inference, that allow you to reach conclusions in certain situations. You may use these (see page 49 of the course notes) to guide your thinking, or as marginal notes to justify certain steps: conjunction elimination: If you know A ^ B , you can conclude A separately (or B...
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This note was uploaded on 10/13/2011 for the course COMPUTER S CSC 165 taught by Professor Dannyheap during the Fall '10 term at University of Toronto Toronto.
 Fall '10
 DannyHeap
 Computer Science

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