Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 3.1, Problem 7E
Program Plan Intro
To prove that
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Let A and B be two finite sets such that n(A) =
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20, n(B) = 28 and n(A u B) = 36, then n(A N B)
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Let X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} are two
sets. find R = {(x, y): x e X and y e Y and (y –
{x) is divisible by 6
. Let Q, R and S be sets. Show that (R – Q) ∪ (S – Q) = (R ∪ S) – Q.
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Introduction to Algorithms
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- et X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} are two sets. find R = {(x, y): x ∈ X and y ∈ Y and (y – x) is divisible by 6}arrow_forwardProve: If a set A is a subset of the empty set, then A itself has to be an empty set.arrow_forwardDe Morgan’s laws also apply to sets. De Morgan’s laws (A U B)’ = A’ ∩ B’ (A ∩ B)’ = A’ U B’ Prove the following using set identities, including De Morgan’s laws A – (A – B) = A ∩ Barrow_forward
- L = {w ∈ {a, b}∗ | the length of w is a multiple of 3 and w contains more a’s than b’s}. Use Myhill-Nerode to prove that L is not regular.arrow_forwardIs A a subset of B if; A = {5,2,1} B ={ 6, 1, 2arrow_forwardOn S = f2; 4; 6; 10; 12; 20; 30; 60g we work with the divisibility relation R:xRy , x divides y:(i) Find all non-empty subsets U S, so that 6 is an R-lowerbound of U.(ii) Let A = f6; 10; 12g. If A admits an R-supremum, nd it. If A admits an R-in mum, nd it.(iii) Is R a lattice?arrow_forward
- How do we define that a function f(n) has an upper bound g(n), i.e., f(n) ∈ O(g(n))?arrow_forwardSuppose A and B are sets, and A is uncountable. Prove that A∪B is uncountable. Theorem 1: Any subset of a countable set is countable.arrow_forward· Tonsider a set S of 4 elements. Prove that we can choose any two subsets óf S of size 3, say A and B, and construct a matroid M = (S, 1) such that A and B are the only maximum independent sets in M.arrow_forward
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