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5. (a) Let S = {a1, @2,. ..,an} denote a finite set. Let C denote a collection of m sibsets of S, ie., C = {S1,S2,...Sm}. where each S, C S. We are interested in the following question: Is there a collection of subsets from C, such that the union of the sets in this collection is S and the cardinality of the collection is at most K? Is this query NP-complete? (b) Let S = {a, az2,...,an} denote a finite set. Let C denote a collection of m subsets of S, ie., C = {S1. S2,...Sm}. where each S, C S. We are interested in the following problem: Is there a partition of s into two subsets R and T, such that no set in C is completely contained in either R or T? Prove that this problem is NP-complete.

5. (a) Let S = {a1, @2,. ..,an} denote a finite set. Let C denote a collection of m sibsets of S, ie., C = {S1,S2,...Sm}. where each S, C S. We are interested in the following question: Is there a collection of subsets from C, such that the union of the sets in this collection is S and the cardinality of the collection is at most K? Is this query NP-complete? (b) Let S = {a, az2,...,an} denote a finite set. Let C denote a collection of m subsets of S, ie., C = {S1. S2,...Sm}. where each S, C S. We are interested in the following problem: Is there a partition of s into two subsets R and T, such that no set in C is completely contained in either R or T? Prove that this problem is NP-complete.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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5. (a) Let S = {a1, a2, ...,an} denote a finite set. Let C denote a collection of m subsets of S, i.e., C = {S1, S2,... Sm}, where each S, C S. We are interested in the following question: Is there a collection of subsets from C, such that the union of the sets in this collection is S and the cardinality of the collection is at most K? Is this query NP-complete? (b) Let S = {a, az2,...,an} denote a finite set. Let C denote a collection of m subsets of S, i.e., C = {S1, S2,..Sm), where each S, C S. We are interested in the following problem: Is there a partition of S into two subsets R and T, such that no set in C is completely contained in either R or T? Prove that this problem is NP-complete.
Transcribed Image Text:5. (a) Let S = {a1, a2, ...,an} denote a finite set. Let C denote a collection of m subsets of S, i.e., C = {S1, S2,... Sm}, where each S, C S. We are interested in the following question: Is there a collection of subsets from C, such that the union of the sets in this collection is S and the cardinality of the collection is at most K? Is this query NP-complete? (b) Let S = {a, az2,...,an} denote a finite set. Let C denote a collection of m subsets of S, i.e., C = {S1, S2,..Sm), where each S, C S. We are interested in the following problem: Is there a partition of S into two subsets R and T, such that no set in C is completely contained in either R or T? Prove that this problem is NP-complete.
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