Discrete Mathematics

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Xnjgune_153

Computer Science

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i want someone who is expert in Discrete mathematics for computer science to solve me some problems .

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2 Problems 1. Let A and B denote two sets. Argue that (a) P(A) P(B) = P(ANB). (b) (P(A) U P(B)) CP(AUB). Give an example where the inclusion is proper. 2. (a) Let A and B denote two countable sets. Is AU B necessarily countable? Justify your answer with a proof or a counterexample. (b) Argue that any subset of a countable set is countable. 3. (a) Let A, B and C denote three sets, where A, B and Care subsets of a set S. Prove that (AUC)[(An B)U(C'n B)] = An B. (6) Among a bank's 214 customers, 189 have checking accounts, 71 have regular savings accounts, 114 have money market savings accounts and 69 have both checking and regular savings accounts. No customer is allowed to have both regular savings and money market savings accounts. How many customers have a checking account but no savings account? 4. (a) Show that if 4 numbers are chosen from the set {1,2,3,4,5,6), at least two of them will sum to 7. (b) Let n be a positive number. Show that in any set of (n + 1) numbers, there are at least two with the same remainder, when divided by n. 5. (a) How many distinct binary operations can be defined on a set of n elements? (b) Consider the set of binary strings of length 8. How many strings in this set contain two or more Os?
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