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Discrete Mathematics Review Question September 24

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Sample Question 1 Terms and Definitions * There is no need for you to remember everything but just understand what it means Example: What’s the meaning of Projection? A. Function that combines n-ary relations that agree on certain fields B. Function that conditionally picks n-tuples from a relation C. Function that produces relations of smaller degree from an n-ary relation

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Sample Question 2 Combining Relations *Give you relations R 1 and R 2. Need you to define like … Example: R 1 = {(a,b) on R 2 | a > b} R 2 = {(a,b) on R 2 | a < b} {(a,b) on R 2 | a != b} R 2 For (a, c) to be in R1 R2, we must find an element b such that (a, b) in R2 and (b, c) in R1. This means that a c. Clearly this can always be done simply by choosing b to be large enough. Therefore we have R1 R2 = R 2, the relation that always holds.

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Sample Question 3 Equivalence proof *Give you a relation, proof why it is a equivalence relation and tell how many equivalence class it has. Example: Suppose we have R ={(a,b) | a b (mod 3)} on set Z +. Proof R is an equivalence relation. * Just proof the reflexive, symmetric and transitive of R. (Text book Section 9.5 Example 3) How many equivalence class it has? * Clearly, 3 ( divided by 3 remain 1,2,0). (Text book Section 9.5 Example 14)

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Sample Question 4 Matrix *Give you a relation represented by matrix, proof why it is a equivalence relation Example: We have a matrix representation of a relation like: [1 0 1] Is this relation a equivalence relation? 2 [0 1 0] List all equivalence class. 3 [1 0 1]

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Ricky Gao TA Office hour Mon & Wed 9:00am – 10:00am at ECSS 3.216

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