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- Which answer is correct?4 1. Define the relation | on N\{0, 1} by a | b precisely when a divides evenly into b. (b) Identify all maximum, minimum, maximal, and minimal elements of |. Prove your result. Note that we are excluding 0 and 1 from the numbers we are considering for the relation. I need help finding the maximum and minimum, maximal and minimal. Thank youIn “Elementary Number Theory & Its Applications” by Kenneth Rosen, in chapter 1.1, the following is defined: The greatest integer in a real number x, denoted [x] is the largest integer function less than or equal to x. That is, [x] is an integer satisfying: [x] ≤ x
- 1. Let Z be the set of integers and let m be a fixed positive integer. Define the relation by xy if and only if m divides x - y (equivalently x - y is a multiple of m). This is called the relation congruence modulo m in Z. (a) Prove that this relation is an equivalence relation. (b) What are the distinct equivalence classes when m = 6? These are also known as the residue classes modulo 6 and the set of these residue classes is denoted by Z6.3) Let the order on the Xe(-002)Q be the Knoun order. find the Sapremum Supremum andinfimum of the set4. Consider the set of all strings of a's, b's, c's and d's. (a) Make a list of all of these strings of length zero, one, and two that do not contain the pattern bb. (b) For each integer n > 0, let sn = the number of strings of a's, b's, c's and d's of length n that do not contain the pattern bb. Find so, s1, and s2. (c) Find a recurrence relation for the sequence s0, S1, S2, . ..
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