# Set Theory, Logic, Probability, Statistics

- Fundamentals: Set theory, logic and proofs. Probability and statistics
 Meta Thread / Thread Starter Last Post Replies Views Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions... Feb23-13 09:25 AM micromass 1 27,680 Hey all, Can anyone prove this theorem? Let N (natural numbers) ---> X be an onto function. Then X is... Nov28-07 12:38 PM Coin 8 2,126 Hey there. I'm asked to prove: If X1,...Xn are random variables defined on a set Ω and B1,...,Bn C R1 then prove... Feb2-12 10:12 PM Kuma 0 1,172 Hello all. I have a question regarding the statement If S(m)=S(n), then m=n, where S(m)=m\cup{m}, the successor of... Nov10-12 09:46 AM StatOnTheSide 2 648 Please take a look at this proof: http://s12.postimg.org/qa24fgbq5/proof.jpg The thing I do not get is how they... Jul10-13 02:43 PM verty 5 650 I recall reading somewhere that the mean value of a continuous variable is situated at a point that acts as a fulcrum... Apr26-12 11:08 PM chiro 10 1,535 Prove the following: If f : A \rightarrow B and g : C \rightarrow D , then f \cap g : A \cap C \rightarrow B... Oct27-07 04:35 PM Jacobpm64 7 3,320 Let: 1) P be one place operation 2) H be two place operation 3) G be two place predicate 4) k, m be two... Nov2-11 10:53 AM solakis 2 901 How do we prove in predicate calculus using the laws of universal end existential quantifiers,propositional... Oct4-08 04:40 PM evagelos 1 1,594 \forall a\forall b\leq b <------>a^{2}\leq b^{2})]. or in words: for all a and for all b , if a>0 and b>0 then ... Dec16-08 11:21 PM MathematicalPhysicist 9 1,640 Let: 1)P be one place operation 2)K be one place operation 3) c be a constant let : Oct31-11 12:04 PM CompuChip 2 1,233 Given : a) 1) c is a constant 2) P and K are one place operation symbols 3) G and H are a two place... Jul19-12 07:34 PM xxxx0xxxx 7 1,390 I am having issues with a proof, as follows. *U = universal set , P(U) = power set of a universal set For all... Apr23-11 10:46 PM arsenal997 2 1,714 Hello Members I am having a little bit of a problem solving this proof for my Discreet math course. If g and f... May30-06 02:06 PM matt grime 1 3,021 Prob.2 Mar24-11 04:33 PM tiny-tim 6 689 Suppose n=ab, show that a^2<=n or b^2<=n. Jan27-09 09:09 PM saadsarfraz 5 853 Hello, This is my first question here. So, lets see how it goes. I need a proof to a simple problem. The proof seems... Oct28-08 05:18 AM CompuChip 1 4,759 Hi, how would you show that 4^(k)+4 * 9^(k) \equiv 0 (mod 5) Jan21-09 02:14 AM Mentallic 22 1,840 X' \cup Y' \subseteq (X \cap Y)' n \in X' \cup Y' n \in X' || n \in Y' (n \in U, n \notin X)||(n \in U,... Jan26-10 11:53 AM nameVoid 0 732 I intend to show, for a set ##X## containing ##A_i## for all ##i##, \overline{\bigcup A_i}\supseteq \bigcup... Oct5-13 02:00 PM Mandelbroth 0 387 I'm supposed to prove that if: n^2 % 3 = 0 Then n % 3 = 0 I'm not sure how to proceed here? Does it got... Feb28-05 02:33 AM Dr-NiKoN 8 1,822 Hello all, I've been asked for a graduate level course to do a proof using induction that shows that nCr always... Oct14-08 06:12 AM D H 38 11,587 I'm to prove that for n>=4, 2^n < n! holds, but I don't know where to go after the inductive hypothesis that it holds... Feb6-12 12:02 PM bryanfoobar 4 22,716 Hello all, I am trying to prove that a set is closed by induction. Specifically, let me define Let B_t be sets,... Apr20-12 10:21 AM submartingale 0 675 Suppose we are asked to prove : If \lim_{n\to\infty}x_{n} = L and x_{n} is decreasing,then \forall n. On the... Jun9-11 07:38 AM micromass 17 2,016 Suppose you have a formal proof of a statement S, but you want to prove a statement S' which is in some way similar to... May16-09 01:58 PM mXSCNT 0 681 Lets say I have \aleph_1 numbers of sets that each have \aleph_1 number of elements and I want to show that the... Aug16-12 01:34 PM Bacle2 9 892 Given sets X1,...,Xn the projection from the product X1 * ... *Xn is the function pri = prxi : X1 * ... *Xn → Xi ,... Mar18-12 06:52 PM Square1 12 2,555 So, I made it to the finals for my fantasy football league. The winner receives $100 and the runner-up$10 (maybe... Dec10-12 06:38 AM jjpbq6 0 634 Hello! I've come here today seeking information about how I can build a ranking system that will sort through some... Aug1-10 06:35 PM CRGreathouse 3 1,287 Dear mates, I run into a difficulty on the captioned area and am looking forward for enlightenments. Consider... May29-07 11:18 AM MWG@berlin 0 4,099 I have always wondered: Is the product rule and addition rule for that matter axioms of the probability theory or... Jul30-13 08:07 PM chiro 2 374 Hi, I am interested in the product of a Gaussian random variable with itself. If X is Gaussian then what is X^2? We... Mar14-11 06:19 AM architect 3 2,645 say, E(1/x)=a and E(y)=b. a and b are constants and x and y are random variables. Can I say E(y/x)=b/a? Thanks. Apr3-10 04:52 PM zli034 2 1,420 Hi, All, Let x1 x2... Xn be correlated random events (or variables). Say P(X1), P(X2)..., P(Xn) can be computed,... Apr23-09 02:13 PM mXSCNT 1 2,419 If you have P(x) distribution and P(y) distribution, then one may write the charactersitic functions of each of these... Jan20-09 06:02 PM natski 0 633 Hi all, I am using a Xi squared test to for independence of two sets of categorical data. So lets say I have a... Oct29-11 12:41 AM Stephen Tashi 1 1,380 If you have a data set which consists of n variables and m factors which are essentially randomly correlated and you... Mar26-09 10:52 AM engineer23 0 1,410 so i'm having problems with logic exercies especially when it asks you to prove long equations like when you just use... Jan24-13 03:35 PM Andrax 2 591 I'm building the circuit for controlling LEDs line with LDR sensor . It can be done by using Many Op-Amp but I... Mar29-09 09:35 PM Vincent90 0 1,082 "Pat arrives at the bus stop at some time U, which is uniformly distributed between time 0 and time 1, and waits for a... Oct30-08 08:05 PM Enuma_Elish 1 1,245