# relation

1. ### Preference relation

Hi everyone, I have been reading this real analysis /economics book and I came across the following problem with which I have been struggling with. If I have two bundles a=(a1,a2) and b=(b1,b2) then I prefer a over b if and only if a1+a2>=0.5+b1+b2 . My question is , is this preference...
2. ### Understanding an Equivalence Relation proof

Hey guys, I asked this question before but now I got the answer from my prof, but I don't really get the answer. A binary relation R is defined on the set Z2 as follows: (a, b) R (c, d) <---> a= c (mod 2) and b = d (mod 3) Here's what I don't get: From the definition, isn't reflexive (x, x)...
3. ### no of reflexive relations on a set cant be 2^(n^2-n).

no of reflexive relations on a set cant be 2^(n^2-n).as we have to take diagnol elements only..so no of reflexive relations are coming out to be n only.if we have a set{1,2,3,4}.then the reflexive relations are only (1,1);(2,2);(3,3);(4,4)..please correct me with reasoning if i'm wrong.
4. ### Prove an Equivalence Relation

Hey, I would like to prove this equivalence relation: A binary relation R is defined on the set Z2 as follows: (a, b) R (c, d) <---> a= c and b = d I know I need to show that R is reflexive, symmetric, and transitive, but I am not sure how in this kind of question.
5. ### Modelling with Recurrence Relation

This is a question from my tutorial. A patient is injected with 80 ml of an antibiotic drug. Every 4 hours 40% of the drug passes out of her bloodstream. To compensate for this an extra 15ml of antibiotic is given every 4 hours. Find a recurrence relation for the amount of drug in the...
6. ### Relation between curvature and torsion

In the context of tensor calculus, by using Serret-Frenet formula or otherwise, how to prove that $\tau^2=\displaystyle\frac{r'''^2}{k^2}-k^2-(\frac{k'}{k})^2$ where $\tau$ and $k$ represent respectively torsion and curvature.
7. ### Proof of inner product relation in a Hilbert space

Hello everyone I have been given a task where I need to prove, \forall \textbf{v} \in H, the following formula: <\textbf{v},\sum \limits^{\infty}_{k=1}c_k \textbf{v}_k>=\sum \limits^{\infty}_{k=1}\bar{c_k}<\textbf{v}_k, \textbf{v} > Where < \: \cdot \: , \: \cdot \: > is an inner product...
8. ### Describe a relation between the composition of two relations and their domains ...

Describe a relation between the composition of two relations and their domains and ranges. Any & all help is appreciated.
9. ### Define the relation R on the set A = {1,7,21,35,36} as: (a, b) ∈ R if GCD(a,b) > 1

Define the relation R on the set A = {1,7,21,35,36} as: (a, b) ∈ R if GCD(a,b) > 1 a. Find three distinct paths from node 36 to node 35. (Use the -> symbol to indicate a transition between nodes.)
10. ### Recurrence relation problem

Hello everyone, I tried to solve this one but it isn't consistent with my solution. How can i solve this problem?

18. ### Limit relation for events

Let (\Omega,\mathcal F,P) be a probability space and (A_n)_{n\ge1} be a sequence of events in \mathcal F. Prove that {{I}_{\underset{n\to \infty }{\mathop{\underline{\lim }}}\,{{A}_{n}}}}+\underset{n\to \infty }{\mathop{\overline{\lim }}}\,{{I}_{A_{n}^{c}}}=1. (Rock)
19. ### what is the symmetric closure of below relations?

If I have a relation ,say ,less than or equal to ,then how is the symmetric closure of this relation be a universal relation . I tried out with example ,so obviously I would be getting pairs of the form (a,a) but how do they correspond to a universal relation.
20. ### what is the reason behind the below nature of the relation?

If I have a relation R which is transitive ,then why is the symmetric closure of the relation is not transitive ?Actually I am confused in this ,so please guide me in this.