lecture7

# lecture7 - Lecture 7 Proofs (cont) Recap Three fundamental...

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Lecture 7 Proofs (cont)

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Recap Three fundamental proof techniques Direct proof Proof by contraposition Proof by contradiction
Warm-up (from last lecture) Prove or Disprove Let n be an integer If n is even, n^2 is even If n^2 is even, n is even

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Prove the following claim Let a and b be two integers, and c = (a+b)/2. Claim: a ≤ c OR b ≤ c
Example Let n be an integer If 3n+2 is odd, n is odd We proved this statement with contraposition. Let’s prove it again with contradiction

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Back to Proofs √2 is irrational
Shortest Paths in Networks

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Network A network is a collection of Nodes (routers), and Links (for direct wireless communication) Let’s give each node a name: n 1 , n 2 ,…, n N , The links are pairs: (n i , n j ) is a link iff nodes n i , and n j can communicate directly
A path is a sequence of nodes where consecutive nodes in the sequence correspond to links P: n 1 , n 7 , n 8 , n 9 . P is an n

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## This note was uploaded on 10/21/2011 for the course CSCI 2011 taught by Professor Staff during the Spring '08 term at Minnesota.

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lecture7 - Lecture 7 Proofs (cont) Recap Three fundamental...

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