What is Discrete math: Definition and 214 Discussions
Discrete Mathematics is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications. It was established in 1971 and is published by North-Holland Publishing Company. It publishes both short notes, full length contributions, as well as survey articles. In addition, the journal publishes a number of special issues each year dedicated to a particular topic. Although originally it published articles in French and German, it now allows only English language articles. The editor-in-chief is Douglas West (University of Illinois, Urbana).
Dear "Physics Forum",
Hello! I'm Sarah. Yeah, I'm new here and starting to love this forum. I'm having a hard time proving if a statement is true or false in discrete math. For example, For all X, there's a Y (x+y=x). This question is easy and the answer is true by letting y as 0 and x for...
Homework Statement
find the domain and image of f such that
f(x) = {(x,y) \in R \times R \vert x = \sqrt{y+3}
and domain and image of g such that
g = { (\alpha,\beta) \vert \alpha is a person, \beta is a person, \alpha is the father of \beta
Homework Equations
the domain and image...
Let A be a set. For every set B and total function f:A->B we define a relation R on A by R={(x,y) belonging to A*A:f(x)=f(y)}
*belonging to - because i don't know how to make the symbole...
Prove that f is one-to-one if and only if the equivalence classes of R are all singletones
Homework Statement
I have to prove the following claim.
Claim: For any positive integers m and n, m and n both greater than 1, if n|m and a≡b(mod m), then a≡b(mod n).Homework Equations
n/aThe Attempt at a Solution
so i first changed each equation (ex: a≡b(mod m)) to a=b+qm and a=b+qn
I...
Hi
I need some help with the following problem:
1. Find all functions f: Z+ -> Z+ such that for each n Є Z+ we have f(n) > 1 and
f(n + 3)f(n + 2) = f(n + 1) + f(n) + 18
2. I've been reading everywhere and I can't seem to find anything like this. I was wondering if anybody knew where to start
3...
From the people I've spoken to, the general consensus is to take the class in separate semesters if possible. What do you guys recommend? I have 3 semesters left before I finish my AA and I want to get as many math courses in as possible...
Thanks.
Hey all,
I just started my Junior year at Florida International University this summer and decided to start light by taking Programming I and Discrete Math to kick things off with and get used to the university. Programming class is going fine, but Discrete Math class is really giving me a...
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
I have two problems that I am having a little trouble with. Thanks in advance.
Homework Statement
Count the number of times the following algorithm prints "Hello", then find the "best" big-oh approximation for the number of print statements in the algorithm.
For i=1 to n
Begin
Print...
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
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...
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...
[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)...
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 reflexive...
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...
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...
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...