Exercise 9 (H.W): a. Show that p n q = qa p and pv q = q v P b. Show that (p v 9) v r = pv (q v r) and (p^ 9^r = p^ (q c. Show that (p ^ 9 v r = (pへ)v(g >) d.Show that (pv r) n (9 v r) and (p v ^r = 9 ^ r = b - vd -=
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- To plot the function f (x) = over [0,5], we use 2x fplot('exp^(-x) /2*x',[0,5]) fplot('exp^(-x)/(2*x)',[0,5]) fplot('exp(-x)/2*x',[0,5]) O fplot ('exp(-x)/(2*x)',[0,5])Let H(x)= " plays hockey". Let B(x) = "x plays basketball". Which statement below means "There is someone who plays hockey and someone who plays basketball"? OVx (H(x) ^ B(x)) Ox (H(x) ^ B(x)) OVx (H(x) V B(x)) OVx (H(x)→ B(x)) 3x (H(x) v B(x)) xH(x)^3x B(x) OVx (B(x) → H(x))Wireless sensor networks (WSNs) refer to a domain of communication networks. In a WSN, small devices called sensor nodes are used for data transfer among each other and a base station. One limitation of a sensor node is that it has a very limited processing capability and very small memory. Consider a scenario in which you have an algorithm that can be subdivided into smaller problems. If you have to run these sub-problems in different sensor nodes, would you prefer to use divide & conquer approach or dynamic programming approach? Write briefly and precisely.
- Implement a program that will populate a 6x5 matrix with randomly generated integers from 100 to 500. (1) print your matrix in a table form. (2) modify your code to multiply all odd numbers by 2 and print the matrix. Sample run: Initial Matrix: 145 | 437 | 222 | 101 | 100 | 278 500 | 190 | 415 | 288 | 466 322 377 | 240 | 451 | 331 186 186 432 102 | 106 | 105 249 248 | 117 | 213 | 499 488 355 | 266 | 396 | New Matrix: 290 | 874 | 222 | 101 | 100 | 278 500 | 190 | 830 288 | 466 322 754 | 240 | 902 | 662 186 432 | 102 | 106 | 210| 498 248 | 234 | 426 | 998 488 710 | 266 | 396 |Prove whether the following argument is valid or invalid. Use methods 1 and 2. 1. p q P→r 2. (р^q) → r →r р q→r :. rProblem Alice was given a number line containing every positive integer, x, where 1<=x<=n. She was also given m line segments, each having a left endpoint, l (1<=l<=n), a right endpoint, r (1<=r<=n), and an integer weight, w. Her task is to cover all numbers on the given number line using a subset of the line segments, such that the maximum weight among all the line segments in the chosen subset is minimal. In other words, let S=(l1,r1,w1),(l2,r2,w2),....,(lk,rk,wk), represent a set of k line segments chosen by Alice, max(w1,w2,...,wk) should be minimized. All numbers 1,2,....n should be covered by at least one of k the chosen line segments. It is okay for the chosen line segments to overlap. You program should output the minimized maximum weight in the chosen subset that covers all the numbers on the number line, or -1 if it is not possible to cover the number line. Input format The first line of the input contains an integer, n - denoting the range of numbers…
- Let H(x) = " plays hockey". Let B(x) = "x plays basketball". Which statement below means "Everyone plays hockey and everyone plays basketball"? OVx (H(x) ^ B(x)) Ox (H(x) ^ B(x)) OVx (H(x) V B(x)) OVx (H(x)→ B(x)) 3x (H(x) v B(x)) O7xH(r)A=æB(x) OVx (B(x) → H(x)) ○\x H(x) →\B(x) 1Consider a function tetrahedral( ) that computes the n^th tetrahedral number for a given integer n>=0: T(n)= Tri(1)+Tri(2)+Tri(3)+...+Tri(n-1)+Tri(n) where Tri(n) is defined as Tri(n)+1+2+3+...+(n-1)+n a) Implement the function tetrahedral( ) using recursion in order to perform the repeated additions. b) Find an algebraic representation for T(n) that does not require any repeated additions. Implement the function tetrahedral( ) with a one-line definition using this formula.Given A={1,2,3,4,56}, B= {2,4,5,6} and C= (1,6,7} 1. B' U C'=
- Consider the following code: for ( i = 0; i < 20; i++) for (j = 0; j < 10; j++) a[i] = a[i] * j a. Give one example of the spatial locality in the code. b. Give one example of the temporal locality in the code.4x1+4x2+6x3+9x4=03x1+3x5=26x2+5x4+7x5=-46x1+8x4+2x5=54x5+7x2+6x3+8x1=-10Represent the set of equations in a matrix equation, Ax=b, where A is a square matrix and x and b are column vectors. Write the line of code to define matrix A for this problem matlab/octave languageGiven a triplet of integers (X , Y , Z), such that X ≤ Y and Y ≥ Z, we define f(X , Y , Z) to be (X + Y) * (Y + Z). If either X > Y or Y < Z, or both, then f(X , Y , Z) is defined to be 0. You are provided three arrays A , B and C of any length (their lengths may or may not be equal). Your task is to find the sum of f(X , Y , Z) over all triplets (X, Y , Z) where X, Y and Z belong to A, B and C respectively. Output your sum for each test case modulo 1000000007. Input The first line contains a single integer, T, which is the number of test cases. The description of each testcase follows: The first line of each testcase contains 3 integers: p, q and r. These denote the lengths of A,B and C respectively. The second line contains p integers, which are the elements of A The third line contains q integers, which are the elements of B The fourth line contains r integers, which are the elements of C Output Output the required sum modulo 1000000007 for each test case in a new line.…