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Which of the following statements are true? The element (1,2,3,4,5) € Shas order 5. The element...
Consider the following relation R on the set A = {1,2,3,4,5}. R= {(1, 1), (2, 2),...
Consider the following relation R on the set A = {1,2,3,4,5}. R= {(1, 1), (2, 2), (2, 3), (3, 2), (3, 3), (4,4), (4,5), (5,4), (5,5)} Given that R is an equivalence relation on A, which of the following is the partition of A into equivalence classes? Select the correct response. A. P = {{1}, {1, 2}, {3}, {3,4}, {4},{5}} B. P ={{1,2,3,4,5}} C. P ={{1,2},{3,4}, {5}} D. P = {{1}, {2,3}, {4,5}} E. P ={{1,2,3}, {1,5}} F. P= {{1},...
Exercise 4. Consider the permutation group S7. a. Show that the subgroup generated by the element...
Exercise 4. Consider the permutation group S7. a. Show that the subgroup generated by the element (1,2,3,4,5,6) is a cyclic group of order 6. b. Show that the subgroup generated by the element (1,3, 4, 5, 6, 7) is a cyclic group of order 6. c. Show that the subgroup generated by the element (1,2,3) is a cyclic group of order 3. d. Show that the subgroup generated by the element (6, 7) is a cyclic group of order 2....
8 α = (д 1 9 2 5 3 4 5 10 3 6 7 86...
8 α = (д 1 9 2 5 3 4 5 10 3 6 7 86 9 10 2 7 10) 1 4 1 в = (1, 2 3 3 5 4 8 5 2 6 9 7 7 8 4 9 6 10 1 10) 10 8 ү 1 3 2 7 3 9 4 5 1 5 6 7 8 2 9 4 19) 10 1 ө ( 42 2 4 5 4 6 5 2 6 7...
1. Show the steps in order to sort {11,5,6,3,8,1,9,2} using Mergesort algorithm. 2. Show the element...
1. Show the steps in order to sort {11,5,6,3,8,1,9,2} using Mergesort algorithm. 2. Show the element sequences of running Shellsort on the input {15,2,8,1,10,7,4,3,9,11,12,6} at the increments {7, 3, 1}, respectively. 3. Show the steps in details of sorting {15, 2, 8, 1, 10, 7, 4, 3, 9, 11, 12, 6} using quicksort with median-of-three partitioning and a cutoff 3 (if the elements are less than 3, using insertion sort).
def sum_gt_avg(num_list): Implement a function that returns the sum of the numbers in num_list that have...
def sum_gt_avg(num_list): Implement a function that returns the sum of the numbers in num_list that have a value greater than the average value in the list. • Parameters: num_list is a list of numbers (mixed integers and floats) • Examples: sum_gt_avg([1,2,3,4,5]) → 9 # 4+5 sum_gt_avg([1,2,3,-4,5]) → 10 # 2+3+5 sum_gt_avg([-1,-2,-3,-4,-5]) → -3 # -1-2
Define a function called collapse() which takes a list as input. Each element of the list...
Define a function called collapse() which takes a list as input. Each element of the list will either be an integer, or a list of integers. The function should modify the input list by replacing all of the elements which themselves are lists with the sum of their elements. For example: Test Result vals = [1, 2, 3, 4, 5] collapse(vals) print(vals) [1, 2, 3, 4, 5] vals = [1, [2, 3], 4, 5] collapse(vals) print(vals) [1, 5, 4, 5]...
Problem 2. For the following statements, write down whether true or false (No justification needed, and...
Problem 2. For the following statements, write down whether true or false (No justification needed, and for ease of grading, please make it clear what is) (1) (a) xE (b) х€ {{x}} (c) x}€{{x}} (d) } E (2) (a) C 1,2,3 (b) E {1,2,3 (c)E P({1,2,3} (d) n0 (3) (a) 1,2,3 (b) {1,2,3} с {1, 2, 3} (c) An0 (d) AU A (4) a) ZnZ = Z (b) ZUZ 22 your answer Problem 3. List the elements of the following...
I need to create a c++ print function that takes a vector of values ex: <1...
I need to create a c++ print function that takes a vector of values ex: <1 2 3 4 5 6> and prints it in the correct way with the given dimensions. Example 2x3 = [[1,2,3],[4,5,6]] or 3x2 = [[1,2],[3,4],[5,6]]. To make this even more difficult there can be 3 dimensional matrixs. For example for <1 2 3 4 5 6 7 8 9 10 11 12> with dimensions depthXheightXwidth: 2x3x2 = [[[1,2],[3,4],[5,6]],[[7,8],[9,10],[11,12]]]. The depth height and width could be...
Let wE S7 be a permutation which rearranges 7 objects as follows, showing the result on...
Let wE S7 be a permutation which rearranges 7 objects as follows, showing the result on the lower line 2 3 4 6 7 5 5 4 2 7 6 1 3 a) Express was a product of disjoint cycles representing how each object moves Is w an even permutation, or an odd permutation? What is its order? products of disjoint cycles b) Calculate w3, w5 and w' 2 as c) Does there exist T E S7 for which T-lwr...
Determine the order of the coset containing each of the following elements in the respective quotient...
Determine the order of
the coset containing each of the following elements in the
respective quotient groups.
order element quotient group (6,1) Z16 Z18/((4, 13)) (9, 11) Z12 Z18/((6, 13)) (4,3) Z10 U(10)/((6, 7)) (12,9) Z14 * U(14)/{(8, 11))||
Consider the following relation R on the set A = {1,2,3,4,5}. R= {(1, 1), (2, 2), (2, 3), (3, 2), (3, 3), (4,4), (4,5), (5,4), (5,5)} Given that R is an equivalence relation on A, which of the following is the partition of A into equivalence classes? Select the correct response. A. P = {{1}, {1, 2}, {3}, {3,4}, {4},{5}} B. P ={{1,2,3,4,5}} C. P ={{1,2},{3,4}, {5}} D. P = {{1}, {2,3}, {4,5}} E. P ={{1,2,3}, {1,5}} F. P= {{1},...
Exercise 4. Consider the permutation group S7. a. Show that the subgroup generated by the element (1,2,3,4,5,6) is a cyclic group of order 6. b. Show that the subgroup generated by the element (1,3, 4, 5, 6, 7) is a cyclic group of order 6. c. Show that the subgroup generated by the element (1,2,3) is a cyclic group of order 3. d. Show that the subgroup generated by the element (6, 7) is a cyclic group of order 2....
8 α = (д 1 9 2 5 3 4 5 10 3 6 7 86 9 10 2 7 10) 1 4 1 в = (1, 2 3 3 5 4 8 5 2 6 9 7 7 8 4 9 6 10 1 10) 10 8 ү 1 3 2 7 3 9 4 5 1 5 6 7 8 2 9 4 19) 10 1 ө ( 42 2 4 5 4 6 5 2 6 7...
Problem 2. For the following statements, write down whether true or false (No justification needed, and for ease of grading, please make it clear what is) (1) (a) xE (b) х€ {{x}} (c) x}€{{x}} (d) } E (2) (a) C 1,2,3 (b) E {1,2,3 (c)E P({1,2,3} (d) n0 (3) (a) 1,2,3 (b) {1,2,3} с {1, 2, 3} (c) An0 (d) AU A (4) a) ZnZ = Z (b) ZUZ 22 your answer Problem 3. List the elements of the following...
Let wE S7 be a permutation which rearranges 7 objects as follows, showing the result on the lower line 2 3 4 6 7 5 5 4 2 7 6 1 3 a) Express was a product of disjoint cycles representing how each object moves Is w an even permutation, or an odd permutation? What is its order? products of disjoint cycles b) Calculate w3, w5 and w' 2 as c) Does there exist T E S7 for which T-lwr...
Determine the order of
the coset containing each of the following elements in the
respective quotient groups.
order element quotient group (6,1) Z16 Z18/((4, 13)) (9, 11) Z12 Z18/((6, 13)) (4,3) Z10 U(10)/((6, 7)) (12,9) Z14 * U(14)/{(8, 11))||
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