this is discrete mathematics question 1. (3 points) Find all integer solutions to 12x + 30y...
DISCRETE MATHEMATICS Problem 3 (10 points) Use mathematical induction to prove the following statement for all n 21. For full credit, mention the base case (1pt), the induction hypothesis (1 pt) and the induction step (8 pts). 12 22 32
Discrete mathematics question Can you please answe the following question? Please show your answer clearly. et n be a positive integer. Use the Master Theorem to obtain the big-O class for the functions that satisfy the following recurrences. (a) (4 points) g(n) -4g(n/2)+ n b) (4 points) (n) 2f (n/3) 0(n)
Discrete Mathematics Question 1: (a) Use the method of generalizing from the generic particular in a direct proof to show that the sum of any two odd integers is even. See the example on page 152 (4th edition, Discrete Mathematics with Applications) for how to lay this proof out. (b) Determine whether 0.151515... (repeating forever) is a rational number. Give reasoning. (c) Use proof by contradiction to show that for all integers n, 3n + 2 is not divisible by...
HELPPPP!!!! sepcific explanation is best !!! this is discrete mathematics content. 1. Prove, or disprove by finding a counterexample: If a|bc where a,b and c are positive integers then a b or a c. 2. Let n be an odd integer. Show that there is an integer k such that n2 = 8k +1.
Discrete Mathematics. Thank You!! 3. Using the digits 1, 2, 3 and 5, how many 4 digit numbers can be formed if a) The first digit must be 1 and repetition of the digits is allowed? (5 points) b) The first digit must be 1 and repetition of the digits is not allowed? (5 points)
discrete math, use the the formula on the paper m) (C5) How many integer solutions are there to the equation x + y + z = 8 for which... (a) x,y,z are all positive? ht(k-1 (b) x,y,z are all nonnegative? (c) x, y, z are all greater than -3? 1 (balls + boxes-1 I boxes- I +(**) - (saldo
Do in Computing Mathematics or Discrete Mathematics 3. (8 pts) A graph is called planar if it can be drawn in the plane without any edges crossing. The Euler's formula states that v - etr = 2, where v, e, and r are the numbers of vertices, edges, and regions in a planar graph, respectively. For the following problems, let G be a planar simple graph with 8 vertices. (a) Find the maximum number of edges in G. (b) Find...
Discrete Mathematics 5. (4 points) Circle the statements that are true and cross out the statements that are false. (c) Zco 6. List the elements of the following sets, given A (0,1), B (-1,0, 1), and C-(1,2) (a) (3 points) Cx B (b) (3 points) (C × B) × A
Discrete Mathematics 1 Is 1.3232 a rational number Justify your answer. 2. Why is 4,050 a composite integer ? Justify and rewrite it as a product of prime integers 1 Is 1.3232 a rational number Justify your answer. 2. Why is 4,050 a composite integer ? Justify and rewrite it as a product of prime integers
Discrete Mathematics Use the graph to answer the following questions 9 (a) (4 Points) Label one of each of the following parts of the undirected graplh i. Vertex ii. Edge ii. Loop iv. Circuit (b) (4 Points) Find the degree of the follow vertices: i. "g" iii. "?" (c) (2 Points) Find the total degree of the graph (d) (4 Points) Describe, with a list of vertices traveled, a walk from"c" to "b