Questions tagged [relations]
For questions concerning partial orders, equivalence relations, properties of relations (transitive, symmetric, etc), a composition of relations, or anything else concerning a relation on a set.
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Is there any way to solve this problem combinatorically or any other quick method?
Let $A$ = $\left\{ 2 , 3 , 6 , 7 \right\}$ and $B = \left\{ 4 , 5 , 6 , 8 \right\}$ .
Let $R$ be a relation defined on $A \times B$ by
$$
\left( a_{1} , b_{1} \right) R \left( a_{2} , b_{2}\right)\...
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Examining whether the relation "$aRb$ iff $a + 2b \equiv 0 \pmod 3$" is reflexive, symmetric, antisymmetric, or transitive [duplicate]
Have I shown correctly which properties the relation fulfills?
$$aRb \text{ iff } a + 2b \equiv 0 \pmod 3$$
$(1)$ Reflexivity
Set $b=a$
$a + 2a = 3a \equiv 0 \pmod 3$
Hence, the relation is reflexive....
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Set theory terminology: how can I formally describe the type of N:N binary relations that can be represented by two tables?
Usually, many-to-many relationships between two sets/tables X and Y are represented in data systems using a third "join" table, which is a list of pairs of elements from X and Y indicating ...
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Difference between 'elements related to an element' and 'elements to which an element is related' in a relation.
Suppose we define a non symmetric relation R:{1,2,3,4}--->{1,2,3,4}:R={(1,1),(1,2),(1,3),(2,1),(2,3),(3,4),(4,1)}
then is there a difference between 'elements related to an element (say 1) in R' ...
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Types of relations- Reflexive, Symmetric, Transitive, Identity, Universal, Null and Equivalence relations
By the definition of it, it appears that a relation can be an identity relation or a reflexive relation only if the relation is on a single set (ie. it is subset of cartesian product of a set with ...
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Morphisms and relations [closed]
I need some help distinguishing these topics. I find them difficult to visualize, and researching them is also challenging, as there have been the occasional paradoxes…
Correspondences and Morphisms
...
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Do functions "preserve" equivalence relations?
I was doing some introductory level set theory for my intro to topology course and one of the problems assigned was:
I was doing part a) and I noticed that I never used the fact that $f$ is ...
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Isn't this relation NOT antisymmetric?
$$
R=\left\{x{,}\ y\in\mathbb{R}:\ y^2=1-x^{ }\right\}
$$
Since (0,1) and (1,0) satisfy this relation and $1 \ne 0$, am I correct in saying that this relation is actually NOT antisymmetric?
There was ...
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Definitions of argument notation for relations
Is there a standard definition for relation argument notation $R(x)$, for some relation $R \subseteq A \times B$, and if not what are the different definitions used, or at least where can I read about ...
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Definition of Composition of Binary Relations [duplicate]
The following is the definition of the composition of relations taken from Wikipedia:
Why don't we, with the aim of being more general in our defintion, define it as follows:
If R is a relation from ...
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Composing stream homomorphisms "apply f" based on dynamical systems (A, f)
I'm trying to do Exercise 99 of Rutten's The method of coalgebra: exercises in coinduction. It says
For all functions $f: A \to A$ and $g: A \to A$, prove that $$\text{apply}_g \circ \text{apply}_f = ...
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What is the difference between a strict partial order and a strict weak order?
According to Wikipedia, strict partial orders and strict weak orders are transitive binary relations satisfying asymmetry, antisymmetry and irreflexivity. See screenshot below:
However, if strict ...
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Can we only define Composite Functions & not Composite Relations in general (where the relation may not necessarily be a function)?
I was reading composite functions in a calculus book. Is a composite relation, let's say not a function in this case, always well-defined? If yes, why do we not lay emphasis on this? If not, what are ...
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How do you clearly and concisely describe the union of a particular function's outputs for one of many functions?
I'm writing research and I've encountered quite a specific problem. The following are example sentences I came up with to try to explain a particular concept. Note that the following is analogous to ...
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Is there a Relation for Exponentiation Similar to $\leq$ or $\backslash$ (divisibility)?
I'm trying to define common mathematical options on the natural numbers.
I am doing this because operations like subtraction are commonly constructed as just the addition of the inverse, however this ...
