Discrete math Definition and 206 Threads

Prove for all sets A,B, and C : A complement UNION B complement = (A intercept B) complement help me out here please

I apologize for the title, I really don't know how to describe these problems, so I just listed the categories that they fall under. Anyways... Homework Statement Let f: A->B be a function, where A and B are finite sets and |A| =|B| (they have the same size I believe). Prove that f is...

From experienece, are these two courses really important to someone looking to major in physics? I've read the "So you want to be a physicist" guide, but if I work with the book Mathematical Methods in the Physical Sciences, will it be enough to make it through the upper level physics courses...

Rewrite the following statement formally. Use variables and include both quantifiers \forall and \exists in your answer. Statement: Every rational number can be written as a ratio of some two integers. If I didn't have to use \exists I'd write it as follows \forallrational numbers...

Homework Statement Definition: let R be an equivalence relation on a set X. A subset of X containing exactly one element from each equivalence class is called a complete set of representatives. now define a relation R on RxR by (x,y)R(u,v) <---> x^2 + y^2 = u^2 + v^2. You don't have to...

[SOLVED] Discrete Math - Complete set of representatives Homework Statement At what temperature fahrenheit is it equal to celsius? Homework Equations (none) The Attempt at a Solution

Quick Summary: I'm in a class were we analyze code / find big theta / Oh / etc (Algorithm Design and Analysis). It's based on discrete math, which I'm terrible at. After posting Tired of Discrete Math... I have come to the conclusion that I will be needing some help figuring out a way to pass...

Rant Warning I am a computer science major and math is a major part of our curriculum. A year ago I took my first ever discrete math course, and it honestly fried my brain. Now I'm in a computer science course that uses discrete math to analyze algorithms, and my brain has simply shutdown...

Homework Statement Show that if n is a positive integer, then 1\,=\,\binom{n}{0}\,<\,\binom{n}{1}\,<\,\cdots\,<\,\binom{n}{\lfloor\frac{n}{2}\rfloor}\,=\,\binom{n}{\lceil\frac{n}{2}\rceil}\,>\,\cdots\,>\binom{n}{n\,-\,1}\,>\,\,\binom{n}{n}\,=\,1 Homework Equations I think this proof involves...

Could someone help me with this induction proof. I know its true. given any integer m is greater than or equal to 2, is it possible to find a sequence of m-1 consecutive positive integers none of which is prime? explain any help is greatly appreciated thanks

Homework Statement Use mathematical induction to show that given a set of n\,+\,1 positive integers, none exceeding 2\,n, there is at least one integer in this set that divides another integer in the set. Homework Equations Mathematical induction, others, I am not sure The...

DISCRETE MATH: Prove a "simple" hypothesis involving sets. Use mathematical induction Homework Statement Prove that if A_1,\,A_2,\,\dots,\,A_n and B are sets, then...

Homework Statement 2. Let A, B and C be the following sets: A = (x є N | x< 25) B=(x e N | x = 2m for some positive integer m) C = (x є N | x = 3m for some positive integer m) Find each of the following sets. In each case, list all of the elements of the set. i) A – (B u C) ii)A n C...

Homework Statement 1. Let x and y be positive integers and assume that xy is odd. Prove the following statement using the method of proof by contradiction: Both x and y are odd. 2. Let A, B and C be the following sets: A = (x є N | x< 25) B=(x e N | x = 2m for some positive...

Homework Statement Use the logical equivalences p \rightarrow q \equiv \sim p \vee q and p \leftrightarrow q \equiv (p \rightarrow q) \wedge (q \rightarrow p) to rewrite the statement form: (p \rightarrow (q \rightarrow r)) \leftrightarrow ((p \wedge q) \rightarrow r) Homework Equations...

Homework Statement f: B => C and g: A => B 1. If f of g is injective, then f is injective. 2. If f of g is injective, then g is injective.Homework Equations The Attempt at a SolutionI know that 1 is true and 2 is false because I found those as properties, but I am not exactly sure why, and...

Homework Statement Use rules of inference to show that if \forall\,x\,(P(x)\,\vee\,Q(x)) and \forall\,x\,((\neg\,P(x)\,\wedge\,Q(x))\,\longrightarrow\,R(x)) are true, then \forall\,x\,(\neg\,R(x)\,\longrightarrow\,P(x)) is true. Homework Equations Universal instantiation, Disjunctive...

Homework Statement Determine whether the argument is correct or incorrect and explain why. A) Everyone enrolled in the university has lived in a dormitory. Mis has never lived in a dormitory. Therefore, Mia is not enrolled in the university. B) A convertible car is fun to drive. Isaac's car...

Homework Statement Determine whether \forall\,x\,(P(x)\,\longleftrightarrow\,Q(x)) and \forall\,x\,P(x)\,\longleftrightarrow\,\forall\,x\,Q(x) are logically equivalent. Justify your answer. Homework Equations P\,\longleftrightarrow\,Q is only TRUE when both P and Q are TRUE or...

Homework Statement Are these system specifications consistent? "(A)Whenever the system software is being upgraded, users cannot access the file system. (B)If users can access the file system, then they can save new files. (C)If users cannot save new files, then the system software is not...

C(n,1) ... I know that C(n,0) =1 But have no clue how to figure out C(n,1) :cry:

Hi, I would like some help for the following problems. please bear with me with my special notation: I- intersection U- union S- universal set ~- complement I need to prove that: let be A and B two sets. prove (A U B) I (A I (~B))=A what I did is: (A U B) I (A I (~B)) =[(A I B)...

Hi, Please can someone help me with this problem. show that a,b,c are real numbers and a#0, then there is a unique solution of the equation ax+b=c. the uniqueness of the solution is my problem. Thank you B

I am in discrete math class right now and trying to get the sets of numbers straight. So, does the set of integers include 0? Is it ok to use 0 in proofs, that makes finding a counter-example a lot easier and disprove a statement about all integers. Was just wondering if that is legal...

Question 1 -------------------------------------------------- "Prove that if (d_1, d_2, ... d_n) is a sequence of natural numbers whos sum is even (n>=1) then there is a pseudograph with n vertcies such that vertex i has degree d_i for all i=1,2,...n" So we have a sequence of natural...

Question: "Find a recurrence relation and initial conditions for the sequence {a sub n} if a sub n is the number of bit strings of length n that contain three consecutive 0's." So here's what I have so far... n > 3 n = 4, 1000, 0001 n = 5, 10000, 00001, 00010, 01000, 10001 n = 6...

One of the class objectives is to give an oral presentation to the professor. This time it has to do with explaining Permutations and Combinations. We have 4 things we need to explain: 1) Permutations / Repetitions are not allowed / Order Matters 2) Combinations / Repetitions are not...

"Six men and 6 females are to be seated around a circular table. Every person must be sitting opposite of another person of the same sex. How many different seatings are possible?" * Ok here's my logic, If you have 12 people, and just want to seat them, you can do so in 11! ways... * So...

I am planning on self studyint Discrete Math. What would be a good book for this?

How useful is the knowledge of discrete math for computer programmers?

How useful is discrete math to an electrical engineer; particularly how useful is it to an ic designer?

[Discrete Math] f: A-->B; surjective? find necessary & sufficient condition. Ok in practice for my discrete exam, I have the following problem. Let f : A->B be a function. a) Show that if f is surjective, then whenever g o f = h o f holds for the functions g,h : B -> C, then g =h. b)...

[SIZE="1"]Ok; this is another thread that covers two questions. I didn't want to mix them with my previous post; it's from the same 'section' but the questions are different. If any mods have issues with this, please say so. 1) If R \cup S is reflexive, then either R is reflexive or S is...

Ok so here's one of the questions we've been assigned... So I can graphically see what this relation looks like, and from that I've shown it's reflexive. Now I'm working on proving it as being symmetric, but I can't put it into words. b) ~ is symmetric. Well we want to show that aRb ->...

Ok so I have two propositions; for ALL x: (P(x) or Q(x)) and I have... (for ALL x: P(x)) or (for ALL x: Q(x)) I need to show if these are logically equivalent. My original assumption was that these are <=>; but that turned out to be wrong. I'm clueless as to what to do... Some hints or...

Ok so I need to prove (by contradiction) that... if the power set(A) is a subset of power set(B), then A is a subset of B. I was given a hint to use proof by contradiction, but in general I'm lost as to what to do... I know the power set of (A) is {B|B subset A} and the powerset of (B) is...

Hi, This is one of the question from my hw, i don't even understand what it's asking? Please shed some light on it.. thx what is the smallest value of k such that any integer postage greater than k cents can be formed by using only 4-cent and 9-cent stamps? Show that k cents in postage...

Hello, How do I proove : (A U B) x (A U B) = (A x A) U (B x B) if and only if : (A C B) or (B C A) ? Please Advice, Dimitry Haritonov

I have a question from hw, the question is stated "Show that if the poset (S,R) is a lattice then the dual poset (S,R^-1) is also a lattice" I know by Rosen theory that the dual of a Poset is also a poset but how can i prove that it is also a lattice, what def. am i missing. Any help would be...

could someone show me how u would solve 2^27841 mod 34 by hand? I know what theorm to use, I am just having trouble using it? Thanks

Hey if anyone could help me with this I would be sooo grateful. I am trying to grasp the idea of onto, one-to-one and bijection(both) functions. A sample problem is: If f(x) = 2x . What is f(Z), all integers. What is f(N), all naturals. What is f(R), all real. These are 3 different problems...

My life is miserable already first week into grade 12. This stupid book they have given is like Socrates, it asks questions but it only gives ugly pictures and more questions. The examples barely relate to the questions, and our Master Teacher only does examples. Of course I am not a brilliant...

1) The board of directors of a pharmaceutical corporation has 10 members. An upcoming stockholder's meeting is scheduled to approve a new slate of company officers (chosen from the 10 board members). A) 4 (Presendent, Vice Presendent, secretary, and treasurer) positions needs filled. How many...

I don't know why but these types of problems always seem to kick my butt. Any how here they are and my best guesses as to the correct answer. 1. Danny has 12 different lures in his tackle box that he takes on a five day fishing trip. On each day of the trip he fishes with the same...

There are a few areas I wanted to make sure I understand what is going on in with discrete math. I have a test tomorrow over these topics and so this is not exactly homework unless you count studying for a test as homework. In any case I will do my best to explain what I know or don't know and...

ok the problem is Given that a and x are intergers, a>1, a|(11x+3), a|(55x+52), find a. I am not sure how to even start this one to find a...any help please :cry:

Prove that for any vectors a and b, |a-b| is less than or equal to |a| + |b| I'm kind of lost, b/c i can't see a case where |a-b| would actually result in a value being less than |a| + |b|. I've tried doing a proof that is similar, and when I was taught, the definition of absolute value...

Discrete Math Help! Here is the problem: Suppose a, b, and c are integers and x, y, and z are nonzero real numbers that satisfy the following equations: \dfrac{xy}{x+y}=a and \dfrac{xz}{x+z}=b and \dfrac{yz}{y+z}=c . Is x rational? If so, express it as a ratio of two integers...

How do you find the angle between the co-ordinate axis (i.e. the xz plane) and another plane in general?

Would anyone happen to have some links which briefly explain some of the laws in geometry and/or discrete math? At the moment, i am looking for a summary of the Properties of Circles . Thank you for being as helpful as you always are. -- ps I found MathWorld, although i can not find...