Problem 10Assume n is an even integer and assume there are n students in class. We want to form as many aspossible clubs such that:(a) each club is of even size, and(b) the intersection of every two clubs is also of even size.Prove by Rank-Nullity Theorem that there are at most 2″/2 such clubs.

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Answered: Problem 10 Assume n is an even integer…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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This question is related to unique factorisation in the Gaussian integers. In the Gaussian integers, find the gcd of 13 and 8 + i. The problem says "the gcd" (which is correct), but what are all the possibilities for the gcd?
a. #5 Prove that for all integers n, it is the case that n is even if an only if 3n is even. That is, prove both implications: if n is even, then 3n is even, and if 3n is even, then n is even. b. #7 Consider the statement: for all integers a and b, if a is even and b is a multiple of 3, then ab is a multiple of 6.Then state the converse, tell if it is true, and prove or disprove.
plz solve the question 3 with explanation. i will give you upvote.
Suppose that a number x is to be selected from the real line R, and let A, B, and C be the eventsrepresented by the following subsets of R, where the notation {x : −−−} denotes the set containingevery point x for which the property presented following the colon is satisfied:A = {x : 1 ≤ x ≤ 5}B = {x : 3 < x ≤ 7}C = {x : x ≤ 0} Problems: 1.2) Toss a coin 4 times. Let A denote the event that a head is obtained on the first toss, and let B denote the event that a head is obtained on the fourth toss. Is A ∩ B empty? 1.3) Consider rolling a six-sided die once. Let A be the set of outcomes where an odd number comes up. Let B be the set of outcomes where a 1 or a 2 comes up. Calculate the sets on both sides of the equalities (Ac ∩ Bc) c = A ∪ B and (Ac ∪ Bc ) c = A ∩ B and verify that the equalities hold. 1.4) We are given that P(A) = 0.55, P(B) = 0.35, and P(A∪B) = 0.75. Determine P(Ac ) and P(A∩B). 1.5) Out of the students in a class, 60% are geniuses, 70% love chocolate and 40% fall…
Consider the list of numbers: 2n-1, where n first equals 2, then 3, 4, 5,6,…What is the smallest value of n for which 2n -1 is not a prime number. Show all your work.
(1). Prove that adding an irrational number with a rational number is an irrational number, and show whether that is true for multiplication.? (2). Study each of the following in temms of being finite - countable - finite - then find the max, min, upper bound, lower bound, sup and inf for each of the following: 1. A= (-4, 4), 2. В- [0,1], 3. С- Q. 4. D={1,2,...,100}, 5. E- (x: -3 sxs3, XEQ)
This is a report already, I deleted question 3 since it was answered already and now I want an answer for question 4 thank you
If X is a positiive integer divisible by 6, and X<60 What is the greatest passibve vaive of X 7
7. The number t₁ = 1 + 2 + +n is called the nth triangular number (so called because t, dots may be inserted in an orderly fashion in an equilateral triangle; the fourth triangular number is familiar to bowlers). Some triangular numbers are also squares (which means that the dots may be rearranged into a square), for example, tg = 6²,149 = 35². Show that there are infinitely many numbers that are simultaneously triangular and square. this is a number theory problem
3) For any non negative integer n , prove that a – bħ is divisible by a-b,where a and b are any integers with a ± b.

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