4.) For each given k, determine the number of commutative binary operations that exist on a...
5. (3, 4, 3 points) Let A-a, b, c, d, e, f, g (a) how many closed binary operations f on A satisfy Aa, b)tc b) How many closed binary operations f on A have an identity and a, b)-c? (c) How many fin (b) are commutative? 6. 10 points) Suppose that R and R are equivalent relations on the set S. Determine whether each of the following combinations of R and R2 must be an equivalent relation. (a) R1...
1. Determine whether * is a binary operation on the given set. If it is a binary operation, decide whether it is associative and commutative. Justify your answers. a. Define * on Q+ by a *b = b. Define * on N by a*b = %.
Determine the output of each algorithm below the number of assignment operations in each (show work) the number of print operations in each (show work) the complexity of each algorithm in terms of Big O notation (show work) 2. Let n be a given positive integer, and let myList be a three-dimensional array with capacity n for each dimension. for each index i from 1 to n do { for each index j from 1 to n/2 do { for...
True or false for each, and explain why (4 pts) The height of a binary tree is bounded by O(n2), where n is the size of the C. tree. d. (4 pts) dynamic array and O(1) time if L is a linked list. Given a list L of n > 2 elements, the following code takes O(n) time if L is a iterator i = L. iterator () i.next); i.next); i.remove ); binary tree T that has size n and...
I. Let each of R, S, and T be binary relations on N2 as defined here: R-[<m, n EN nis the smallest prime number greater than or equal to m] S -[< m, n> EN* nis the greatest prime number less than or equal to m] (a) Which (if any) of these binary relations is a (unary) function? (b) Which (if any) of these binary relations is an injection? (c) Which (if any) of these binary relations is a surjection?...
Question 2. Recall that a monoid is a set M together with a binary op- eration (r,y) →エ. y from M × M to M, and a unit element e E/, such that: . the operation is associative: for all x, y, z E M we have (z-y): z = the unit element satisfies the left identity axiom: for all r E M we have the unit element satisfies the right identity axiom: for all a EM we Let K...
k Determine whether the rule describe a function with the given domain and target. You must provide a specific counterexample if you determine it is not a function. (Note that the symbol squareroot refers to the principal or positive square squreroot .) f:R rightarrow R where f(x) = sqaurerootx f:Z rightarrow where f(n) = squaretrootn^2 + 1 For c, d and e below, consider the function: f: {0,1}^n rightarrowZ (i.e., f maps elements from the set of all bit strings...
Prove that the number of unordered sequences of length k with elements from a set X of size n is n+k−1 k . Hint: For illustration, first consider the example n = 4, k = 6. Let the 4 elements of the set X be denoted a, b, c, d. Argue that any unordered sequence of size 6 consisting of elements a, b, c, d can be represented uniquely by a symbol similar to “··|·|··|·”, corresponding to the sequence aabccd....
for the specific random numbers n, m, and k obtained, an undirected graph Gn,m,k = (Vn,m, En,m,k) is defined as follows. Vn,m= {A | A is a subset of {1,2, .., n} and |A|= m}, E n,m,k={{A, B} | A∩B | = k} where | A | for the set A denotes the number of elements of A. (A) Illustrate G4,2.1. (B) Find the number of vertices and sides of G6,3,2. (C) Find the condition for n so that Gn,3,1...