4. Let n be a positive integer with n > 20, and let S (1,2.. n21 with IS- (a) Show that S possesses two different 3-element subsets, the sums of whose elements are equal b) Show that S possesses t...
,n2} with ISI = n. 4. Let n be a positive integer with n > 20, and let S {1, 2, -I with a) Show that S possesses two dilferent 3-element subsets, the sums of whose elements are equal. (b) Show that S possesses two disjoint subsets, the sums of whose elements are equal ,n2} with ISI = n. 4. Let n be a positive integer with n > 20, and let S {1, 2, -I with a) Show that...
Let n be a positive integer with n > 20 , and let with 1. Show that S possess two disjoint subsets, the sum of whose elements are equal. S 1,2,., 1n2) We were unable to transcribe this image
3. (20 pts) Let ụ be a finite set, and let S = {Si, S , S,n} be a collection of subsets of U. Given an integer k, we want to know if there is a sub-collection of k sets S' C S whose union covers all the elements of U. That is, S k, and Us es SU. Prove that this problem is NP-complete. 992 m SES, si 3. (20 pts) Let ụ be a finite set, and let...
4. Ranking/Unranking Subsets. Let A be a set of n elements and set Sk(A) be the collection of all k-element subsets of A. Recall that |Sk(A)I - (a.) (8 points) Describe a ranking algorithm to rank a k-element subset of an n-element set. (b.) (8 points) Describe an unranking algorithm to unrank an integer 0 < s< [into a ithm to unrank an integer 0 S s <C) k-element subset of an n-element set. (c.) (10 points) As examples, let...
I got a C++ problem. Let n be a positive integer and let S(n) denote the number of divisors of n. For example, S(1)- 1, S(4)-3, S(6)-4 A positive integer p is called antiprime if S(n)くS(p) for all positive n 〈P. In other words, an antiprime is a number that has a larger number of divisors than any number smaller than itself. Given a positive integer b, your program should output the largest antiprime that is less than or equal...
Question 9: Let S be a set consisting of 19 two-digit integers. Thus, each element of S belongs to the set 10, 11,...,99) Use the Pigeonhole Principle to prove that this set S contains two distinct elements r and y, such that the sum of the two digits of r is equal to the sum of the two digits of y. Question 10: Let S be a set consisting of 9 people. Every person r in S has an age...
1. (Integers: primes, divisibility, parity.) (a) Let n be a positive integer. Prove that two numbers na +3n+6 and n2 + 2n +7 cannot be prime at the same time. (b) Find 15261527863698656776712345678%5 without using a calculator. (c) Let a be an integer number. Suppose a%2 = 1. Find all possible values of (4a +1)%6. 2. (Integers: %, =) (a) Suppose a, b, n are integer numbers and n > 0. Prove that (a+b)%n = (a%n +B%n)%n. (b) Let a,...
20 -{24R/1<x<1+ }}-(1,1+ 4) for each positive integer S: = ? a. US = ? i=1 4 b. O S = ? 11 c. Are S1, S2, S3, ... mutually disjoint? Explain. d. ÜS; = ? =1 72 e. n S = ? 1-1 00 f. US = ? 00 g. S; = ?
5-13 please Homework on sets 1. let the universe be the set U (1,23. .,1.0), A (147,10), B- (1,2 list the elements for the following sets. a. B'nt C-A) b. B-A c. ΒΔΑ 2. Show that A (3,2,1] and B (1,2,3) are equal 3. Show that X Ixe Rand x > 0 and x < 3j and ( 1,2) are equal. 5. Use a Ven diagram and shade the given set. (cnA)-(B-Arnc) Show that A (x| x3-2x2-x+2 O) is not...
4. Determine cos2 (20)de where n is a positive integer. a. Determineſ cos(20) de. Show your work. (3 points) b. Determine Scos* (20)do. Show your work. (3 points) c. Determine Scos (20)de. Show your work. (3 points) d. Determine cos2n (20)do. (4 points)