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CSE115/ENGR160 Discrete Mathematics 04/26/12 Ming-Hsuan Yang UC Merced * * * * * * * 9.3 Representing relations Can use ordered set, graph to represent sets Generally ...
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CSE115/ENGR160 Discrete Mathematics 02/14/12 Ming-Hsuan Yang UC Merced * * * * * * * * * 2.2 Set operations Union: the set that contains those elements that are ...
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CSE115/ENGR160 Discrete Mathematics 02/17/11 Ming-Hsuan Yang UC Merced * * * * * * * * * * * * * * * * * 2.3 Functions Assign each element of a set to a particular ...
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... matrices are better choice Suppose that R is a relation from A={a1, a2, ... Example Powers Rn Representing relations using digraphs Example Example ...
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CSE115/ENGR160 Discrete Mathematics 03/20/12 Ming-Hsuan Yang UC Merced *
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... or the law of detachment * Example If both statements If it snows today, then we will go skiing and It is snowing today are true.
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Title: CS173: Discrete Math Author: Cinda Heeren User Last modified by: mhyang Created Date: 8/25/2005 3:39:22 AM Document presentation format: On-screen Show (4:3)
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Title: CS173: Discrete Math Author: Cinda Heeren User Last modified by: mhyang Created Date: 8/25/2005 3:39:22 AM Document presentation format: On-screen Show (4:3)
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... n=10 Related to big-Omega and big-Theta notations in algorithm design * Big-O notation Let f ... is big-oh of g(x) * Big-O notation The constants C and k are ...
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Title: CS173: Discrete Math Author: Cinda Heeren User Last modified by: mhyang Created Date: 8/25/2005 3:39:22 AM Document presentation format: On-screen Show (4:3)
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CSE115/ENGR160 Discrete ... we will show there are unsolvable problems The problem is the halting problem * The halting problem It asks whether there is a ...
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Title: CS173: Discrete Math Author: Cinda Heeren User Last modified by: Chih-Yuan Created Date: 8/25/2005 3:39:22 AM Document presentation format
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CSE115/ENGR160 Discrete Mathematics 04/26/11 Ming-Hsuan Yang UC Merced * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 8.1 Relations and their properties ...
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... functions Example Example f and f-1 Graphs of functions Example 2.4 Sequences Sequences Geometric progression Arithmetic progression String Special integer ...
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CSE115/ENGR160 Discrete Mathematics 04/14/11 Ming-Hsuan Yang UC Merced * * * * * * * * * * * * * * * * * * * Example Among 100 people there are at least 100/12 ...
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... functions Example Example f and f-1 Graphs of functions Example 2.4 Sequences Sequences Geometric progression Arithmetic progression String ...
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CSE115/ENGR160 Discrete Mathematics 03/17/11 Ming-Hsuan Yang UC Merced * 3.6 Integers and algorithms Base b expansion of n For instance, (245)8=2*82+4*8+5=165 ...
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* Permutation How many ways can we select 3 ... r-permutation r-permutation r-permutation Example Combinations r-combination Example r-combination r ...
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CSE115/ENGR160 Discrete Mathematics 02/01/11 Ming-Hsuan Yang UC Merced * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1.6 Direct proofs of p q ...
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CSE115/ENGR160 Discrete Mathematics 05/03/12 Ming-Hsuan Yang UC Merced * * * * * * * * * * * 9.4 Equivalence relation In traditional C, only the first 8 characters of ...
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CSE115/ENGR160 Discrete Mathematics 04/24/12 Ming-Hsuan Yang UC Merced * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 9.1 Relations and their properties ...
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CSE115/ENGR160 Discrete Mathematics 01/18/11 Ming-Hsuan Yang UC Merced * * * * * * * * * * * * * * * Example Let p denote The automated reply can be sent Let q ...
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CSE115/ENGR160 Discrete Mathematics 04/19/12 Ming-Hsuan Yang UC Merced * * * * * * * * * * * * 8.1 Recurrence relations Many counting problems can be solved with ...
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OpenGL uses the modeling part of the model-view matrix to convert from the ... Cavalier. DOP makes 45deg. angle with the proj. plane. Cabinet: DOP makes a 63.4deg. ...
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So, We conclude that if x and y are distinct positive real numbers, then their arithmetic mean is greater than their geometric mean * Example Suppose that two ...
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