Let A = {x EZ|x = 6a+ 4 for some integer a), B = {yEZ y = 18b-2 for some integer b), and C = {zEZ|z=18c+ 16 for some integer c). Prove or disprove each of the following statements. a. ACB b. BCA c. B = C
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- Let A = {a, b, c} and B = {u, v}. Write a. A × B b. B × AProgram the following using SageMath Python:Use Sage ) to write a program that williteratively calculate kR for a point R on an elliptic curve E modulo n where k ≥ 2. You’lluse this program in the elliptic curve method problem on this assignment.• Remember that in the elliptic curve method for factorization, we are actively looking fora ZeroDivisionError, so you might want to use “try—catch” in order to catch this errorif it occurs in the calculation.Complete the following methods
- Let A = {k, {k, z), {k}, {p}, z}. %3D 1. JA| = %3D 2. Which of the following statements are true? There may be more than one correct answer. OA. {p} E A OB. z E A OC. {z} E A OD. k E A OE. Ø E A OF (k, z} E A OG. (k} E A OH.p E A 3. Which of the following statements are true? There may be more than one correct answer. OA. (z} CA B. z CA OC. {k} C A OD. (k, z} CA OE. p CA OF. (p} CA OG. k CA OH.ØCAGiven L = {w = {a, b}*: |w| is even}, the correct statements are: (aa U ab Uba U bb)* is a regular expression that generates L. (ab Uba)* is a regular expression that generates L. aa U ab U ba U bb is a regular expression that generates L. ab U ba is a regular expression that generates L.Assume that a, b, c are numbers.Return 'increasing' if they are in increasing order, 'decreasing' if they are in decreasing order, 'both' if they are both increasing and decreasing, and 'neither' otherwise.Here, 'increasing' means that each value is at least as largeas its predecessor. Similarly for decreasing.The sequence 3, 4, 4 is increasing. whereasthe sequence 4, 4, 4 is both increasing and decreasing.For example,lenient(3, 4, 5) returns 'increasing'lenient(3, 4, 4) returns 'increasing'lenient(4, 4, 4) returns 'both'lenient(4, 3, 2) returns 'decreasing'lenient(4, 3, 3) returns 'decreasing'lenient(4, 2, 3) returns 'neither'
- Let p be the statement "I celebrate" and q be the statement "Bangladesh wins". [Hint: The following statements express p→q:“if p, then q”, “p implies q”, “if p, q”, “p only if q”, “only if q, p”, “p is sufficient for q”, “a sufficient condition for q is p”, “q if p”, “q whenever p”, “q when p”, “q is necessary for p”, “a necessary condition for p is q”, “q follows from p”, “q unless ¬p”] c). Which of the following expresses contrapositive of p→q?. 1. I am sad whenever Bangladesh loses. 2. Only if Bangladesh loses, I am sad. 3. I am sad only if Bangladesh loses. 5. A necessary condition for me to be sad is Bangladesh's loss.Consider the following statement: Vx (2+1 x-1) =X Over the domain of integers, is the above statement true or false? (Enter the whole word "true" or "false".) A If you answered false, give a counterexample (enter your A counterexample as an integer):Let p be the statement "I celebrate" and q be the statement "Bangladesh wins". [Hint: The following statements express p→q:“if p, then q”, “p implies q”, “if p, q”, “p only if q”, “only if q, p”, “p is sufficient for q”, “a sufficient condition for q is p”, “q if p”, “q whenever p”, “q when p”, “q is necessary for p”, “a necessary condition for p is q”, “q follows from p”, “q unless ¬p”] d)Which of the following expresses inverse of p→q?. 1. Bangladesh loses whenever I am sad. 2. Only if I am sad, Bangladesh loses. 3. Bangladesh loses only if I am sad. 4. A necessary condition for Bangladesh to lose is my sadness.
- Please answer it in Python Suppose we play a game where each round takes place in the following way: first, we roll a dice, and its result gives the number of points at stake. Then, the player can, if he wishes, trigger his bonus "double account" or his bonus "triple account". Then, the player answers a number of questions, and calculates his percentage of correct answers. The points awarded to the player for that round are then calculated based on the percentage of correct answers and the number of points in play rounded to the nearest integer (for example, with 50% correct answers and 6 points in play, the player gets 3 points; with 45% correct answers and 8 points in play, the player gets 4 points). Finally, this number of points is possibly multiplied by two or three if the corresponding bonus has been used. Write a function points_match that takes as an argument the percentage, the number of points at stake, and as an optional argument the multiplier (which is worth 2 in a double…Let p be the statement "I celebrate" and q be the statement "Bangladesh wins". [Hint: The following statements express p→q:“if p, then q”, “p implies q”, “if p, q”, “p only if q”, “only if q, p”, “p is sufficient for q”, “a sufficient condition for q is p”, “q if p”, “q whenever p”, “q when p”, “q is necessary for p”, “a necessary condition for p is q”, “q follows from p”, “q unless ¬p”] The following four questions are all based on the paragraph above. You have to answer all of them in order to be able to click the submit button down below. a) Which of the following expresses p→q?. 1.Bangladesh wins whenever I celebrate. 2.Only if I celebrate, Bangladesh wins. 3.Bangladesh wins only if I celebrate. 4.A necessary condition for Bangladesh to win is my celebration.Recall our discussion in class about vacuous truth. (“All of the pages in my hand are green.") Of the following statements, which one(s) is/are vacuously true? [Important note: The question is not asking you to find all of the true statements, but to identify only the ones that are vacuously true.] (a) For all integers n, if n 16, then n 2 4 (d) For all integers n, if 5n > n, then n 20 (e) For all positive integers m, if m < 5, then m² < 25 (f) For all positive integers m, if m < 1, then m2 <1