Discrete mathematics Definition and 100 Threads

Homework Statement Determine the dom(g) Homework Equations Let 'f' be a relation on ℤ (the set of integers) , defined by the entrance requirement : (x;y) ∊ ƒ iff y = x + 15 and let 'g' be the function on ℤ defined by the entrance requirement : (x;y)...

Homework Statement Question 1 : a) Use Venn diagrams to determine whether or not, for all subnets A,B and C of a universal set U, (A-B) ∪ C = (A∪C) - (A∩B) b) If the statement appears to hold, give a proof, if not, give a counter example. Homework Equations (A-B) ∪...

Question 2: -------------------- Homework Statement Consider the following sets, where U represents a universal set : U = {1, 2, 3, 4, ∅, {1}} A = {1, 3} B = {{1}, 1} C = {2 , 4} D = { ∅ , 1, 2 } Homework Equations A+D is the set : (Choose only one ) 1. {1, 3}...

Question 1 : -------------------- Homework Statement Consider the following sets, where U represents a universal set : U = {1, 2, 3, 4, ∅, {1}} A = {1, 3} B = {{1}, 1} C = {2 , 4} D = { ∅ , 1, 2 } Homework Equations Choose the correct option : D - B is the set ...

Homework Statement The Question data is as follows : Consider the following sets, where U represents a universal set : U = {1, 2, 3, 4, ∅, {1}} A = {1, 3} B = {{1}, 1} C = {2 , 4} D = { ∅ , 1, 2 ) Homework Equations Which one of the following statements is true ? 1. The...

I've been having trouble finding many pure math Ph.D. programs with active research groups in the general field of discrete mathematics (perhaps due to its interdisciplinary nature). I'm only aware of the top schools in this field (e.g. Carnegie Mellon, Georgia Tech, UCSD, Rutgers); can anyone...

Q 1. On a circular island we build n straight dams going from Sea to sea, so the ever two intersect but no three go through the same point. Use Euler’s Formula to determine how many Q 2. Into how many parts do two quadrilaterals divide the plane, If (a) They are convex (b) They are not...

Homework Statement Question 1: a) Suppose you have brought four pens of different colours to the exam. For each of the ten question on the exam, you choose one pen. In how many ways can this be done? b) In how many ways can you distribute six bananas and five oranges between three children...

Homework Statement For every non-negative integer z, z2 - 3z is an even integer. Prove this statement. So far, I have learned about direct proofs and indirect proofs such as contraposition and contradiction. Homework Equations An integer z is odd when there is an integer a so that z = 2a+1...

Ok, so I'm having difficulty adapting to subjects like set theory etc. For example this question: L.{A,a} = {A, a, b, ab, ba, aba} Find L Now, I know the answer but it was a battle getting there. It took me 30 mins before giving up and turning on my PC. I got annoyed so much that...

None of my advanced courses require discrete math as a requisite. In fact, the only course that does explicitly require it is not on my degree plan of operations research. However, is this going to bother me when it comes time for say Real Analysis, Advanced Calc, or Abstract Algebra? I think...

Homework Statement There are 17 street lamps along a straight street. In order to save electricity and not affect the regular use at the same time, we can shut down 5 of these lamps. But we cannot turn off a lamp at either end of the street, and we cannot turn off a lamp adjacent to a lamp...

Homework Statement There are 17 street lamps along a straight street. In order to save electricity and not affect the regular use at the same time, we can shut down 5 of these lamps. But we cannot turn off a lamp at either end of the street, and we cannot turn off a lamp adjacent to a lamp...

Discrete Mathematics -- Symmetric Closure Math help in Numerical Analysis, Systems of I can't seem to find the way to approach this problem. Because it has symbols I don't know how to type here, I have attached an image here instead. Please help me if you can. Any input would be greatly...

Hi, i have studied discrete math and there are topics like linear algebra and analytic geometry and googling i found that there are not in other courses, what are the topics in your discrete math courses?

Discrete Mathematics - (A∪B)-(A∩B)=(A-B)∪(B-A) - prove by cases?? Hi, I'm new to these forums so please redirect me if I've posted this in the wrong place. I'm trying to graduate and this is my last class, but as I'm not a math major, I'm really struggling with this particular problem. I've...

Hi all, I am going to be taking Discrete Mathematics in August and my last Math course was about 5 years ago. I am a little intimidated to just 'jump' back into Math especially a course like this one. Can anyone who was successful give me a few pointers? I ordered the Textbook and will...

Hi guys! I got really stuck with a Discrete Mathematics homework in Integers and Algorithms. I know it is not very clear due to lack of symbols. If anyone didn't understand some part of the exercise I would like to clarify it. The exercise is the following : Homework Statement Define for B...

Homework Statement For all n ∈ Z+, the function Pn of i variables is defined recursively as follows: Pn(x1,...,xn) = Pn-1(x1 + x2, x2 + x3,...,xn-1 + xn) and P1(x1) = x1. Find a closed formula for Pn. Homework Equations Pn(x1,...,xn) = Pn-1(x1 + x2, x2 + x3,...,xn-1 + xn) and P1(x1)...

I am starting a maths major and I will going to go into pure maths. I am going to specialize in either analysis or discrete maths. I understand that mathematical analysis has a very strong connection to calculus and that discrete mathematics is used mainly in the cryptography and security...

Ex 36, p 147. Let f be a function from the set A to the Set B. Let S and T be the subset of A. Show that b) f(S \cap T) \subseteq f(S) \cap f(T). Thanks.

Homework Statement Which is larger, square root of 2 or cubed root of 3? Prove one is larger than the other without using decimal approximations for either number. The Attempt at a Solution I attempted to solve this through the contradiction that they were even. If they are not even then...

Apparently everyone uses either Discrete Mathematics and Its Applications by Kenneth H. Rosen or Discrete Mathematics with Applications by Susanna S. Epp. Are these really the best ones? Both are very long texts which make me think they're not rigorous and they're descriptive like Stewart’s...

Homework Statement Find a formula for when m \sum k=0 the flooring function of[k1/3 ] ,m is a positive integer. Homework Equations n\prod j=m aj The Attempt at a Solution the flooring function of[k1/3] = K the summation of K is \frac{m(m+1)}{2} There's a table of...

Hello all, I am stuck on some homework, basically I am stuck on the problems dealing with proofs. I am not asking for complete answers just any direction would be helpful. 1) I have to prove the Grötzsch graph is not 3-colorable (vertex can be colored in such a way that no edge shares 2...

Hello, I'm looking for a decent Discrete Mathematics book.. Well, - Discrete Mathematics & Its Applications. - Discrete Mathematics With Its Applications. Are the top-sellers and the top-rated books @ Amazon on this field. Has anyone read any of them? Recommendations? Pros & Cons? I'm...

Homework Statement a.) F = {(1, a), (2, b), (3, a), (4, c)} G = {(b, 1), (a, 2), (c, 3)} i. Find F o G ii. Find G o F b.) A function F: N x N --> N is represented 2(m + n) + 1 for F(m, n) i. Is F one-to-one? ii. Is F onto? c.) Prove by Mathematical Induction...

Homework Statement Prove that for all integers a >= 1, a^n - 1 is divisible by a - 1 for all n >= 1. Homework Equations None. The Attempt at a Solution Proof - Let P(n): a^n - 1 is divisible by a - 1, then P(1): a^1 - 1 is divisible by a - 1 is TRUE since a^1 - 1 = a - 1, and...

Describe an algorithm that takes as input a list of n distinct integers and finds the location of the largest even integer in the list or returns 0 if there are no even integers in the list. Please Help me on how to solve this type of question I am clueless.

Homework Statement a 1= 2, a k+1, 2ak-1 Homework Equations What is the 5th term The Attempt at a Solution a1= 2 a2=2(2)-1= 3 a3=2(3)-1=5 a4=2(4)-1=7 a5=2(5)-1=9 5th term =9?

Prove or disapprove that the product of two rational numbers is irrational How do you solve this? Thanks

page.130 Ex.20 Ex.20 Show that if A and B are sets, then (A\capB) \bigcup (A\capB) = A. how do u solve this? The Attempt at a Solution

I know I have to write an equation to solve the problem down. But I really don't know how to use the given information. I did it by enumeration, but I don't get it how this will be shown by an algebriac argument. Please some one help me at least with an idea. If S = {1,2,3,4}, consider the...

Dear all, I have an example taken from the book titled "Discrete Mathematics For Computer Science" by Kenneth Bogart. In the book, page 11, example 1.2-2, it says: Write down all the functions from the two element set {1,2} to the two element set {a,b}. I couldn't understand the...

Hi, Im after some advice on what materials to use in order to gain a fairly 'decent' understanding of the following topics: Elementary Set Theory, Subsets, Unions, Intersections, Complements. Logic, Functions, Mappings, Injectivity. Subjectivity. Bijectivity, Permutations, Proof techniques...

Homework Statement Find the range of the function g: ZxZ --> ZxZ given by g(m,n)=(m-n,m+n). Hints: First recall that if f: A ---> B then Range (f)={b e B such that there exists an A in A with b=f(a). Second, if you claim that some set C is the range, then you must show that i) C is a subset...

Homework Statement An electronic switch bank consists of a row of six on - off switches. How many different settings are possible if exactly three of the switches are set to off? (a) 12 (b) 144 (c) 60 (d) 30 (e) 20 Homework Equations Factorial rule...

Homework Statement A certain state issues a series of automobile license plates such that each license plate must have 2 letters followed by three digits. An example license plate would be AD 025 . If the letters and the digits cannot be repeated, how many different license plates can be...

[SOLVED] Propositional logic Discrete Mathematics Homework Statement Assuming atleast one of the following statements is true, which one is it? why? a. Exactly one of these statements is true b. Exactly two of these statements are true c. Exactly three of these statements are true d...

Homework Statement For all integers m, m^{}2=5k, or m^{}2=5k+1, or m^{}2=5k+4 for some integer k. Relevant equations I'm pretty sure we have to use the Quotient Remainder THM, which is: Given any integer n and positive integer d, there exists unique integers q and r such that...

Homework Statement Prove the following statement: For all real numbers x and y, |x| times |y| = |xy| Homework Equations I really don't know how to start this as a formal proof. The Attempt at a Solution I was thinking I'd have to break it down into four cases and logically prove...

Homework Statement Suppose a, b, and c are integers and x, y, and z are nonzero real numbers that satisfy the following equations: xy/(x+y)=a xz/(x+z)=b yz/(y+z)=c Is x rational? If so, express it as a ratio of two integers. Homework Equations I substituted a lot of equations...

Geometry and Discrete Mathematics notes?? Resources? Hello everyone, I'm going to take Geometry and Discrete Mathematics, next year in high school (grade 12). So this summer I'm planning to read some books that would help me out next year, to bulit up my basic skills. So anyone know any sites...

Let \Sigma = { \beta,x,y,z} where \beta denotes a blank, so x\beta \neq x, \beta \beta \neq \beta, and x\betay \neq xy but x \lambday = xy. Compute each of the following: 1: \parallel \lambda \parallel 2: \parallel \lambda \lambda \parallel 3: \parallel \beta \parallel 4...

I ran into this logic puzzle and have been working on it for couple hours now but i can't seem to explain clearly why the answer i came up with is the answer. Heres the question: The police have three suspects for the murder of Mr. Cooper: Smith, Jones, and Williams. Smith, Jones, and...

Hi, For one of the questions in my Discrete Mathematics course, I have to find what property of a formula makes its dual formula also its negative. With a dual formula, the logical operators of "^" and "v" are reversed, the former meaning "and" and the latter meaning "or". With its negative...

Decision and discrete mathematics... Why is Decision maths called "Decision maths"? :smile: Thanks.

Find the scalar eq'n of a plane that is perpendicular to the plane with normal vector [3,1,2] and passes through points A(2,-6,-1) and B(1,2,-4). I think that the normal vector can be the direction vector of this new plane. But then, in order to find the scalar eq'n I need a normal vector...

Can someone give me a definition of discrete mathematics?

Hey all, I'm having some problems with this one homework question... We just did The Intersection of Three Planes using The augmented matrix... and here's my question... For what value of k will the following set of planes intersect in a line? x - 2y - z = 0 x + 9y - 5z = 0 kx - y + z = 0