Q2: Anethe following subsets defien a partition anZ? A-?x:x is an integer multiple of 49 Brx:x-1...
5. Let R denote the set of real numbers. Which of the following subsets of R xR can be written as Ax B for appropriate subsets A, B of R? In case of a positive answer, specify the sets A and B. (a) {(z,y)12z<3, 1<y< 2}, (b) {z,)2+y= 1), (c) {(z,y)|z= 2, y R), (d) {(z,y)|z,yS 0}, (e) {(z,y) z y is an integer).
I need help with these linear algebra problems. 1. Consider the following subsets of R3. Explain why each is is not a subspace. (a) The points in the xy-plane in the first quadrant. (b) All integer solutions to the equation x2 + y2 = z2 . (c) All points on the line x + z = 5. (d) All vectors where the three coordinates are the same in absolute value. 2. In each of the following, state whether it is...
Question 5 16 pts Let set A = {a,b,c} Which of the following are proper subsets of A? {a} a, b {a, b} {a,b,c} {d} Question 6 10 pts Let A = {ne Z | n = 6a + 4 for some integer a} Let B = {me Z m = 18b - 2 for some integer b} Prove or disprove that ASB Hint: follow the method used in Example 6.1.2 on page 338 of the text. HTML Editora B...
4) Let D be the set of all finite subsets of positive integers. Define a function (:2 - D as follows: For each positive integer n, f(n) =the set of positive divisors of n. Find the following f (1), f(17) and f(18). Is f one-to-one? Prove or give a counterexample.
Consider the following four problems: Bin Packing: Given n items with positive integer sizes s1,s2,...,sn, a capacity C for bins and a positive integer k, is it possible to pack the n items using at most k bins? Partition: Given a set S of n integers, is it possible to partition S into two subsets S1 and S2 so that the sum of the integers in S1 is equal to the sum of the integers in S2? Longest Path: Given...
4. (25 points) Which of the following subsets of R3 are subspaces.Explain. a) {(x, y, z) 1 x 0, y 0, z ? c) {(z, y, z) | x2 + y2 + z2-1} d) Is the set H of all matrices of the form |(a,0)T, (b,d)T] a subspace of the space of all 2x2 matrices with the usual matrix addition and scalar multiplica- tion?
,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...
Java 8 9m left Jav 27 28 ALL 29 0 Given an integer array, separate the values of the array into two subsets, A and B, whose intersection is null and where the addition of the two subsets equals the entire array. The sum of values in set A must be strictly greater than the sum of values in set B, and the number of elements in set A must be minimal. Return the values in set A in increasing...
8) (Problem 17 (a) on page 49) Let p and q be two distinct primes. Show that for any integer a, pq|(a p+q − a p+1 − a q+1 + a 2 ). Hint: Find the least residue of a p+q − a p+1 − a q+1 + a 2 modulo p, and then find the least residue of a p+q − a p+1 − a q+1 + a 2 modulo q. After that, use the following result: Suppose x,...
Q2. Answer the following questions assignment, you will develop a well-documented pseudocode that generates all possible subsets of a given set T (i.e. power set of T) containing n elements with the following requirements: your solution must be non-recursive, and must use a stack and a queue to solve the problem. For example: ifT- {2, 4, 7,9; then your algorithm would generate: U, t2), (4;, {7), {9;, 12,4), 12,7;, 12.9;, 14,7), 14,9), 17,9;, ...etc. (Note: your algorithm's output need not...