Set theory Definition and 438 Threads

This is more to see if I understand it or not. There are four statements and I need to explain why they are true. (they all are) I understand it why some of they are, but my answers just don't feel accurate/formal enough. Homework Equations 1) \mathbb{R}^3 \subseteq \mathbb{R}^3 2)...

Prove that if g\circf is surjective, then g must be surjective. I know that one valid proof of this statement is acquired via the contrapositive, what I am not sure of is if the following proof is flawed (if it is, please say why): Suppose z\inZ. Since g \circ f is surjective, there exists...

Polynomial Function. Homework Statement f:ℝ→ℝ x→x^2+x+2 Homework Equations Prove that: f(ℝ)=[7/4,+∞[ The Attempt at a Solution Well I don't know how answer this, so can someone give me a clue on how to start it off?

Homework Statement Prove that if A is a subset of B then A/D is a subset of B/D. Homework Equations The Attempt at a Solution Consider element x of A. Since A is a subset of B then for all x element of A, x is an element of B. Consider element x of A/D. If x is an element of D...

Homework Statement {1/x+1/y / (x,y) in (IN*)^2} subset of ]0,2] Homework Equations The Attempt at a Solution When x=y=1 u get a sum of 2 which is in ]0,2] and for any x and y greater than 1 u get a sum between 0<sum≤2. It's a simple problem but i just don't know how to show the...

Homework Statement Basically, I'm given the probability of 4 independent events: P(A) = 0.04 P(B) = 0.03 P(C) = 0.02 P(D) = 0.01 If anyone of these occur, a failure will happen. More than one can happen at the same time. I need to find the probability that more than one of them...

How are ordinal numbers in set theory/order theory related to ordinal numbers in English? There should somehow be a bit of relationship for them to share the same name.

Homework Statement Let A = A1 x ... x An B = B1 x ... x Bn C = C1 x ... x Cn Such that A,B,C are non empty, A=B\cup C and B\cap C = \emptyset prove that there exists a k in {1,...,n} such that B_k\cap C_k = \emptyset and for i\neq k, A_i = B_i = C_i Homework Equations...

Homework Statement Prove that if P(A) \subseteq P(B) then A \subseteq B, where A and B are two sets and P symbolizes the power set (set of all subsets) of a particular set. Homework Equations The Attempt at a Solution Okay, so here goes. Because it's a conditional, we suppose...

Homework Statement f: X -> Y is a map from X to Y. And A, B subset X are random subsets of X. Proof the following: a) if A subset B then f(A) subset f(B) The Attempt at a Solution (1)Take an arbitrary element x in f(A). (2)For every x there has to be a y in A so that f(y)=x (3)From A...

Homework Statement The universal set u=40 Set A = 20 Set B=17 n(A∩B) = 1/2n(A'∩B') What is the value of n(A∩B)? Homework Equations none^^The Attempt at a Solution The first thing I thought was that because Set A and Set B add up to 37 there must be 3 remaining outside the two sets, and since...

I've never been exposed to this axiom schemata of replacement before, so here's my understanding of it: the axiom includes an arbitrary formula, and that formula may have arbitrarily many free variables. Therefore, a separate axiom is needed for formulas with one free variable, with two free...

Homework Statement There are 30 people in a class of which 7 people have black hair and 24 people are right handed. 2 people are neither right handed nor have black hair. 1. How many have black hair and are right handed? 2. How many have black hair and are not right handed? I'm sure this...

Homework Statement If A, B, and C are subsets of the set S, show that A^C \cup B^C = \left(A \cap B\right)^C Homework Equations A^C = \{x \in S: x \not \in A\} A\cup B = \{x \in S:\; x \in A\; or\; x\in B\} A\cap B = \{x \in S:\; x \in A\; and\; x\in B\} The Attempt at a Solution...

in a coaching centre of 70 but 4 students went on a university visit.31 went to unilag,35 went to lasu and 36 went to u.i. 10 went to all the three universities, 12 went to unilag only, 13 also went to lasu only, 15 went to u.i only. how many students visited 1 . . unilag and lasu 2 . .at...

Hello, I am teaching myself Set Theory, and in doing some exercises I came across the problem: Given sets A and B, prove that A \subseteq B if and only if A \cap B = A. My proof, in natural language, is in two parts: 1) Prove that if A \subseteq B, A \cap B = A. By the definition...

Homework Statement Prove where X and Y are both sets use theoretic reasoning i) Z \ (X \cap Y) = (Z \ X) \cup (Z \ Y) ii)(Y \ X) \cup Z = (Y \cup Z) \ (X \ Z) iii) Z \ (Y \ X) = (X \capZ) \cup(Z \ Y) Homework Equations \ = set difference The Attempt at a Solution i know you don't do other...

Homework Statement Find ∪i=0Ai (with infinite symbol) and ∩ i=0Ai (with infinite symbol) in each of the cases when for each natural number i, Ai is defined as: 1. Ai = {i,−i, i + 1,−(i + 1), i + 2,−(i + 2), . . .} 2. Ai = {0, i, 2i} 3. Ai = {x : x is a real number such that i < x...

Homework Statement Is A ∩ C ⊆ B equal (A ∩ C) ⊆ B or A ∩ (C ⊆ B)? Homework Equations N/A The Attempt at a Solution I think it's the first one due to it being in order, but I'm not sure...

Hi! I am looking for a text concerned with NBG axiomatic set theory( Neumann-Bernays-Godel). Could you recommend some books related with it?

Homework Statement Prove that \cup_{x \in C} \{ 2^{x} \} \subseteq 2^{\cup C} Homework Equations \cup_{x \in C} \{ 2^{x} \} = \{ A | \exists x \in C, A \subseteq 2^{x} \} 2^{x} is the powerset of x. i.e. 2^{x} = \{ y | y \subseteq x \} The Attempt at a Solution Suppose A \in...

Homework Statement An auto insurance has 10,000 policyholders. Each policyholder is classified as: (i) young or old; (ii) male or female; (iii) married or single. Of these policyholders, 3000 are young, 4600 are male, and 7000 are married. The policyholders can also be classied as 1320...

If \mathbb{Z} is the set of integers, what does \mathbb{Z/2Z} mean?

Use proof by contradiction to prove the following: Let a be an irrational number and r a nonzero rational number. Prove that if s is a real number, then either ar+s or ar-s is irrational. I am stuck with this proof. Here's what I have so far, Proof Suppose, by way of contradiction, that...

I'm having a problem with providing counter examples when disproving a statement. For example A - (B U C) = (A - B) U (A - C). The solution given was A = {a}, B = {a} and C = empty set. My question is how can you work this out - i was told it's possible from the Venn diagrams but I'm not...

Hi, I've been trying for 3 hours to solve this proof using identities. I can't seem to get it. Can i get a little help please? Prove: A U B = (A ∩ B') U (A' ∩ B) U (A ∩ B) thanks

I am having issues with a proof, as follows. *U = universal set , P(U) = power set of a universal set For all sets A, B, C ∈ P(U), if A ⊆ C and B ⊆ C, then A ⊆ B or B ⊆ A. I am pretty sure the statement is false and so I have to disprove it, i.e. prove the negation. I am stuck on how to...

I need to prove the following: (A-C) U (B-C) = (A U B) - C I know that the union means that I have to do a proof by cases to show that these two sets are equal. But where do I start?! thanks

Hey, I would like to start a discussion about the use of set theory in mathematical physics. I myself have done research in categorical physics and have seen the debates on how it can be an alternate foundation for mathematics. We can discuss here a few things, but try to stick to these...

Homework Statement Can't quite figure out the LaTeX for Indexed Sets, so bear with me: From "Book of Proof" Section 1.8 #11 http://www.people.vcu.edu/~rhammack/BookOfProof/index.html Is the UNION of Aa, where a is in I, a subset of the INTERSECTION of Aa always true for any collection of sets...

Hi, I'm struggling to understand how to approach set theory equality questions for example: True or false? (A n B) is a subset of (A u B) Is quite simple as its obvious the intersection will contain everything that is in the union But what about a more complex question like ...

I'm trying to prove the following: if E is infinite set and F is finite set. prove that E and E U F have the same cardinality ? So what I did: I'm going to use Schroeder-Bernstein Thm. 1st, it's easy to show that |E| is less of equal to |E U F| since it is a subset of this latter. Now...

All elements in \mathcal{A} match all elements of \mathcal{B}. The order of the information in \mathcal{B} is important to understand the dynamics of the information. \mathcal{A} does not have a logical order of information. However \mathcal{B} does have a logical order. Because there is no...

I know all the numbers of a real part of an equation is given as \Re How do you express your complex part in the same form?

Homework Statement Let L be a partially ordered set. Every countable chain in L has an upper bound. Let S be a countable subset of L such that for arbitrary a,b in S there exists a c in S such that a (less-than-or-equal) c and b (less-than-or-equal) c. Prove S has an upper bound in L...

Homework Statement Homework Statement are located in the pdf below. I also upload the file onto an online viewer for pdf for those people who are afraid to download attachments. Here is the link: http://view.samurajdata.se/psview.php?id=c1f5a372&page=1 Homework Equations None.The Attempt...

HI friend , I am confused about how to start set theory , i want to learn it fully, so please help me in choosing books on this topic which covers from very basics to full advance. thanks Sid

Hi, I just found cheap Naive Set Theory by Halmos. I am wondering if it is worth buying. I have read somewhere it helps reading more advanced books. Plus it's small, it's easy to carry around. I do not like to bring heavy bag to the library. I am a Physics major. I have taken Calc...

URGENT HELP PLEASEEEE, a question on set theory Homework Statement the question is: Prove that these sets have cardinality aleph-nought:(there is two 2 prove) (a) {1/(2^k) : k∈ℕ} (b) {x∈ℤ : x >= -5} im not sure how to work this out, please help on this, i did ask on a previous...

set theory question please help it urgent, thank you Homework Statement 1. Homework Statement Let A, B and C be any sets inside our universal set U. Decide whether each of the following statements is true or false. Justify your answers by giving a proof or a counterexample as...

Homework Statement Prove that the fraction m/n occurs in position \frac{m^2 +2mn + n^2 - m -3n}{2} of the enumeration {1/1, 1/2, 2/1, 1/3, 2/2, 3/1,...} of the set Q+ of positive rational numbers. (Hint: Count how many terms precede m/n in the enumeration.) Homework Equations The Attempt...

This problem is from Hrbacek and Jech, Introduction to Set Theory, Third Edition, right at the end of chapter 2. Homework Statement Let A \neq {}; let Pt(A) be the set of all partitions of A. Define a relation \leq in Pt(A) by S_{1} \leq S_{2} if and only if for every C \in S_{1}...

Homework Statement describe exactly when x intersecting (y union z) = (x intersecting y) union z Homework Equations The Attempt at a Solution I just for some reason cannot see this solution and need a shove in the right direction

Solve the paradox of set theory V7.5 by LiJunYu 2010.12.25 email: myvbvc@tom.com or 165442523@qq.com Brief:All power sets of real number set R: P(R),P(P(R)),P(P(P(R))),...,Pn(R),...Because all Pn(R) does not contain its own,in Russell's paradox,"all sets which does not...

What are the best books on Set Theory?? I mean a book with all axioms and theory and dispenses other books.

Homework Statement using set theroetic notation, write down and prove the contra-positive of: GOD WHAT IS WRONG WITH LATEX? It is completely ruining my set notation! And i can't fix it! If B \cap C \subseteq A Then (C-A) u (B-A) is empty. The Attempt at a Solution I'm awful with set...

Homework Statement [A-(BUC)]U[(A\cup B)-C]U[(A\cap C)-B]U[A\capB\capC]; The Attempt at a Solution Sorry about the crappy formatting (btw). Anyway, I'm trying to "prove" that this is is equal to A. So basically cancelling out the Bs and Cs? I'm not sure how to go about this. de...

Hi, I was wondering if anyone had any ideas how to approach this model building exercise. I've got to use set theory to design a discussion group, I'm given two initial sets (Persons and Strings), from this I have to make the following sets: Members - set of members, each member is a...

First Homework Statement Let X be a finite non-empty set and Y a countable set. Prove that XxY (X cross Y) is countable Homework Equations X isomorphic {1, 2, ..., n} for some n\inN, N is natural numbers Y isomorphic to natural numbers The Attempt at a Solution I wasn't able to...

Homework Statement Prove: Let F and G be functions. F = G if and only if domF = domG and F(x) = G(x) for all x \in domF. Homework Equations ? The Attempt at a Solution If F = G, then (xFy if and only if xGy) (Substitutivity of identicals) If (xFy if and only if xGy), then...