Subject Area: Discrete Mathematics / Proofs, Number Theory, Modular Arithmetic and Congruence Classes PROBLEM 2 Prove...
Discrete Mathematics. Question 2: (a) Use modular arithmetic to find 1040 mod 210. Show your working. (b) An RSA cryptosystem uses public key pq = 65 and e = 7. Decrypt the ciphertext 57 9 and translate the result into letters of the alphabet to discover the message.
DISCRETE MATHEMATICS
Problem 3 (10 points) Use mathematical induction to prove the following statement for all n 21. For full credit, mention the base case (1pt), the induction hypothesis (1 pt) and the induction step (8 pts). 12 22 32
PROBLEM 3. Prove or disprove the following: /V2V54 log2 (J18 V ) is an irrational number. PROBLEM 4. Find the number of different symmetric relations that can be defined on a set 1 - {a,b). PROBLEM 5. Let A - {2, 3, 4, 8, 9, 12), and let the relation Ron A be defined by aRb if and only if (abia#b). Find R.
Problem 5. Prove the following result for any number a and discrete random variable X. 티(X-a 21 = Var(X) + (E(X)-a)2 You must start your proof by using the definition of the expected value of a function of a discrete random variable, i.e. where g(x)- (x-a)
Intermed Microecon Theory
please help.
3.4 Problem 4 Suppose we have a 2 person economy, with endowments (w,u2), where is the endowment of personi. You may assume utility functions are monotone and represent concave preferences. Prove the following two claims: . Given a number ii є R, if (zi.r2) = arg max(m (zi) : "tr') 2 i, 팎 + 2 for each good n then (,2) is pareto efficient. In words, if an allocation amximizes the utiltiy of person 1...
please explain thanks
LP problem
3:32 No SIM minimize subject to 224 -3i + 2 1.3 1. Illustrate the feasible area of problem (P) 2.) For the problem (P), use the nonnegative variable x3 for inequality constraint 1 and the nonnegative variable x4 for inequality constraint 2 and the nonnegative variable 5 for inequality 3 to Show the equation standard form of the problem (P). (3) Find all feasible basis solutions of the equation standard form of the problem (P)...
Please do number 2
Assume all matricies are Mmxm(R) unless otherwise specified. 1. (1 point) Prove or disprove that the eigenvalues of A and AT are the same. 2. (2 points) Let A be a matrix with m distinct, non-zero, eigenvalues. Prove that the eigenvectors of A are linearly independent and span R”. Note that this means in this case) that the eigenvectors are distinct and form a base of the space. 3. (1 point) Given that is an eigenvalue...
Prove that x*-(1, 1/2-1) is optimal for the optimization problem (1/2)xTPx + qTr + r -1 xi<1, i-1,2,3, minimize subject to where 13 12-2 22.0 P-12 176 14.5 2 6 12 13.0
Prove that x*-(1, 1/2-1) is optimal for the optimization problem (1/2)xTPx + qTr + r -1 xi
I need help with number 3 on my number theory
hw.
Exercise 1. Figure out how many solutions x2 = x (mod n) has for n = 5,6,7, and then compute how many solutions there are modulo 210. Exercise 2. (a) Find all solutions to x2 +8 = 0 (mod 11). (b) Using your answer to part (a) and Hensel's Lemma, find all solutions to x2 +8 = 0 (mod 121). Exercise 3. Solve f(x) = x3 – x2 +...
specifically on finite
i pmu r the number of objøcts or ways. Leave your answers in fornsiala form, such as C(3, 2) nporkan?(2) Are repeats poasib Two points each imal digits will have at least one xpeated digin? I. This is the oounting problem Al ancmher so ask yourelr (1) ls onder ipo n How many strings of four bexadeci ) A Compuir Science indtructor has a stack of blue can this i For parts c, d. and e, suppose...