Tagged Questions
2
votes
2answers
36 views
Let $A$ be a set, $R$ an empty relation on $A$, what is $A/R$?
Let $A=\{0,1,2\}$ be a set and $R=\{\}$. I know that $R$ is not an equivalence relation, but does it have to be? What is $A/R$ if $R$ is empty?
Examples:
$R_1=\{(0,0),(1,1),(2,2)\}$, $A/R_1=\{[0], ...
2
votes
1answer
43 views
Proving this realtion is not a transitive relation
I have trouble proving how the following statement is false:
The relation $g = \{\,(x,y)\in \Bbb R\times\Bbb R\mid y = x^2\,\}$ is transitive.
I know you have to use $yRx$, $zRy$, and $xRz$, but I'm ...
0
votes
2answers
23 views
Domain of a Relation from A to B
The latest versions of Susanna S. Epp's Discrete Mathematics book (both the First Brief Edition, and the full Applications 4th edition) define a relation from $\mathcal{A}$ to $\mathcal{B}$ as a ...
1
vote
2answers
40 views
Function - Test of Transitivity
Relation R in the set N of natural numbers defined as
R = $\{(x, y): y = x + 5 $and $x < 4\}$
We can make set : (1,6)(2,7)(3,8)
Is this a transitive function please guide..
1
vote
2answers
34 views
Do not understand what this question is asking… or the notation, Discrete Structures/Relations
Let X = {1,2,....,10}
Define a relation R on X x X by (a,b)R(c,d) if a + d = b + c
I lose track of what it is asking on the part italicized.
I have a similar question that ends in ad = bc as well ...
0
votes
1answer
85 views
Relational Sets for Reflexive, Symmetric, Anti-Symmetric and Transitive
I just want to brush up on my understanding of Relations with Sets. Specifically with this set:
$\{ 1, 2, 3 \}$
I understand Reflexive, Symmetric, Anti-Symmetric and Transitive in theory. But if ...
0
votes
3answers
42 views
Relations: Reflexive, symmetric, transitive
I am having difficulties determining if this relation is reflexive, symmetric, transitive, or none of these.
Let A be the set of all strings of $0's$, $1's$, and $2's$ of length $4$. Define a ...
3
votes
1answer
35 views
Counting non-isomorphic relations
On a set $X$ of $n$ elements, how many non-isomorphic relations are there? The number of relations on a set of $n$ elements is $|\mathcal{P}(X \times X)|=2^{n^2}$, but is there any way to give a ...
1
vote
3answers
47 views
Congruence Relation with exponents and variables
I am currently trying to solve a congruence relation with a constant and a variable, both of which have attached exponents. The relation is as follows:
$7^{95}\equiv x^{3} (mod 10)$
How does one ...
3
votes
1answer
47 views
Would some be able to check my work: for a set, how many different relations are there?
I'm not too sure about the work that I have done here and would love if someone would be able to check my work. If it's correct, would you be able to explain the reason it works? (I feel as though I'm ...
0
votes
0answers
26 views
Equivalence relation question [duplicate]
Let $A$ be the set of all bit strings of length 12. Let $R$ be the relation define on $A$ where two bit strings are
related if the first 2 bits, the 4th bit and the 7th bit are the same. Show that $R$ ...
0
votes
4answers
107 views
Proving reflexivity, symmetry and transitivity,…, on a relation on words
The relation R ,$uRv$ is defined iif a word u is the suffix of a word v. u is a suffix of v if there exist another word w such that $v = wu $
I have to verify the 6 following relations.
Reflexive : ...
0
votes
1answer
199 views
Determine whether the relation is reflexive, symmetric, antisymmetric, transitive, and/or a partial order.
Determine whether the relation is reflexive, symmetric, antisymmetric, transitive, and/or a partial order.
$ (x,y) \in R $ if $ x \ge y $ when defined on
the set of positive integers.
I'm not sure how ...
2
votes
1answer
41 views
A problem on partially ordered set
Two different posets cannot have the same Hasse diagram, but they may have the
same cover graph or the same comparability graph. How to prove the first one and show examples of the other cases.
-1
votes
2answers
186 views
Properties of Relations. Reflexive, Symmetric, and Transitive.
Another person who shares both mother and father with you is your full sibling. Is the relation "x S y meaning x is a full sibling of y" reflexive? Is it symmetric? Is it transitive?
5
votes
2answers
90 views
On the Definition of Posets…
In my book, the author defines posets formally in the following way:
Let $P$ be a set, and let $\le$ be a relationship on $P$ so that,
$a$. $\le$ is reflective.
$b$. $\le$ is transitive.
$c$. ...
2
votes
5answers
58 views
A transitive relation $R$ such that $R\circ R\neq R$?
Find an example of a set $A$ and a transitive relation $R$ on $A$ such that $R\circ R\neq R$.
$R\circ R$ is the relation such that $(a,c)\in R\circ R$ when $(a,b) \in R$ and $(b,c) \in R$. I know ...
0
votes
1answer
53 views
Determining If A Relation Is A Function
I am given the simple relation $f(x)=\sqrt{x}$, where $f$ maps $R \rightarrow R$, and I am suppose to determine whether or not it is a function.
I figured that it was a function, because in the ...
3
votes
1answer
94 views
For the relation $R = \emptyset$ on $\{1, 2, 3\}$, is it reflexive, symmetric, transitive?
In the case below, a relation on the set $\{1, 2, 3\}$ is given. Of the three properties, reflexivity, symmetry, and transitivity, determine which ones the relation has. Give reasons.
$R = ...
0
votes
2answers
35 views
Why am I getting that minimal elements are equivalent to the minimum?
I have these two definitions, about minimals and minimums in an order relation:
$b$ is minimal in $B<=>¬\exists:(x \in B \land x \prec b)$ and also equivalent to $ \forall x,[(x \in B \land x ...
1
vote
2answers
77 views
Is cancellation of Cartesian product possible? I think so, but am having trouble with the proof…
So, Is a cancellation possible for the Cartesian product? ex. if you have two Cartesian products that are equal to eachother, do the 2nd sets for each product equal eachother?
Lets say you have ...
0
votes
3answers
45 views
Domain of a function is all the elements of the first set?
I am reading about functions in the textbook "Discrete Mathematical Structures" by Kolman et.al. They have given in an example that
\begin{equation}
A=\{1,2,3\} \quad\text{and}\quad B=\{x,y,z\}
...
2
votes
2answers
312 views
Reflexive , symmetric and transitive closure of a given relation
Given a relation $R = \{(x,y)\mid y=x+1\}$ and I have to find the reflexive, transitive and symmetric closure.
For reflexive, I added $y=x$ with given condition so now the relation becomes
$R = ...
2
votes
1answer
167 views
Is it reflexive: everyone who has visited Web page a has also visited Web page b, for all webpages
This is a question from "Discrete Mathematics and Its Applications":
...
1
vote
2answers
124 views
Relation $R$ is $xy\ge1$, and $x\in \mathbb{Z}$ and $y\in\mathbb{Z}$, is $R$ reflexive?
This is a question from book "Discrete Mathematics and Its Applications".
9.1.7
Determine whether the relation R on the set of all integers is reflexive, symmetric, antisymmetric, and/or ...
2
votes
1answer
265 views
Problem about Hasse diagrams
Can someone help me to solve this problem.
Are these Hasse diagrams lattices?
-2
votes
2answers
66 views
Does complementary relation($\overline R$) is transitive?
Let $R$ be a relation that is transitive. Does complementary of $R$ ($\overline R$) is transitive?($\overline R$is hold transitive)
0
votes
4answers
184 views
Proving reflexivity, symmetry and transitivity on a relation.
I am trying to see if the following relation is reflective, symmetric and transitive:
$(i, j),(k, l)$ are in relation R if:
$(i < k$ $\land $ $k \le j \le l) \lor (k < i$ $\land$ $i \le l \le j ...
0
votes
1answer
66 views
Set Relation question
Let each of $A, B$, and $C$ be a set and suppose $A \subseteq B \cup C$. Prove that $A \cap B \cap C = \varnothing$.
I start this problem by letting $x$ be an element of $A \subseteq B \cup C$ and ...
1
vote
1answer
54 views
Is the relation $\geq$ always a partial order for the real numbers and integers
I was looking at particular examples and I observed that they were always reflective, antisymmetric and transitive.
3
votes
2answers
100 views
Tricky transitive relations
I have a set $A = \{1, 2, 3\}$.
Relation $S = \{(1, 1), (1, 2), (3, 1) \}$
Relation $T = \{(1, 1), (3, 2), (3, 1) \}$
$S$ is not transitive, but $T$ is transitive. Why is that?
A relation $R$ ...
1
vote
1answer
313 views
Relations , Discrete Mathematics: SETS
Let $A = \{a, b, c\}$ and $R = \{(a, c), (b, b), (c, a)\}$ be a relation on $A$.
Determine whether $R$ is reflexive, symmetric, transitive and anti-symmetric, or not.
1
vote
1answer
58 views
How come the relation $\subseteq $ on the power set $2^N$ is antisymmetric?
where $2^N$ is the power set with $n$ elements (subsets).
Does it hold true to any set or just the power set $2^N$?
2
votes
2answers
229 views
Answering Questions For A Poset.
The question I am looking at is, "Answer these questions for the poset $(\{3,5,9,15,
24,45\},|)$."
a) Find the maximal elements.
b)Find the minimal elements.
c) Is there a greatest element?
d) Is ...
1
vote
3answers
267 views
Reflexive Transitive Closure
The problem I am working on is, "Show that a finite poset can be reconstructed from its covering relation. [Hint:Show that the poset is the reflexive transitive closure of its covering relation.]"
I ...
0
votes
1answer
51 views
Establishing A Covering Relation
The problem I am working on is, "What is the covering relation of the partial ordering $\{(A,B)|A⊆B\}$ on the power set of $S$, where $S=\{a, b, c\}$?"
I am reading the answer key, and I can follow ...
0
votes
1answer
557 views
Constructing A Hasse Diagram Using The Covering Relation
I am still having a little difficultly with the covering relation, specifically that when y covers x, $x \prec y$ there is no element in between them, $ x \prec z \prec y$, where x,y, and z are ...
0
votes
3answers
94 views
Definition Of Lexicographic Ordering
I am reading about about lexicographic ordering, and I want to make sure I am understanding it properly. Lexicographic ordering is defined to be the cartesian product of two, or more, posets. So, $A_1 ...
2
votes
1answer
136 views
Incomparable Elements In A Poset
The problem I am working on is, Find two incomparable elements in these posets.
a) $(P(\{0,1,2\}),⊆)$
b) $(\{1,2,4,6,8\},|)$
For a, I said that $R \subseteq p(\{0,1,2,3\}) \times p(\{0,1,2,3\})$, ...
1
vote
1answer
112 views
Warshall's algorithm multiple choice…
Here's a question given to us for practice.
Can anyone help me through the steps of solving it? The algorithm itself is confusing to read, so I'm just looking for a concise way to calculate $W_1$, ...
0
votes
1answer
53 views
Finding Upper And Lower Bounds
The question is, Find the lower and upper bounds of the subsets $\{a, b, c\}$, $\{j, h\}$, and $\{a, c, d, f\}$ in the poset.
A poset is of the form $(S,R)$, where $S$ is the set, and $R$ is the ...
1
vote
3answers
255 views
How to show that two equivalence classes are either equal or have an empty intersection?
For $x \in X$, let $[x]$ be the set $[x] = \{a \in X | \ x \sim a\}$.
Show that given two elements $x,y \in X$, either
a) $[x]=[y]$ or
b) $[x] \cap [y] = \varnothing$.
How I started it is, if ...
1
vote
2answers
83 views
Dual Of A Poset
The question I am working on is, "Find the duals of these posets.
a) $(\{0,1,2\},≤)$
b) $(\Bbb Z,≥)$
c) $(P(\Bbb Z),⊇)$
d) $(\Bbb Z^+,|)$
In my textbook, they say to find the dual of a poset, ...
3
votes
1answer
189 views
Determining If A Relation And Set Can Form A Poset
The question is, "Is $(S,R)$ a poset if $S$ is the set of all people in the world
and $(a, b)∈R$, where a and b are people, if
a) a is taller than b?
b)a is not taller than b?
c) $a=b$ or a is an ...
1
vote
3answers
98 views
Intuitive understanding of relations and their basic properties
Can anyone explain relations and the four basic properties of them (reflexive, symmetric, antisymmetric, transitive)- or direct me to a source that does.
Particularly, are these statements ...
2
votes
2answers
261 views
Determing If Relations Are Partial Orderings
The question is, "Which of these relations on$\{0,1,2,3\}$ are partial orderings? Determine the properties of a partial ordering that the others lack."
The only two I had trouble with were:
...
2
votes
3answers
49 views
Disjoint Equivalence
Why do equivalence classes, on a particular set, have to be disjoint? What's the intuition behind it? I'd appreciate your help
Thank you!
1
vote
1answer
296 views
Maximal and Minimal Elements
In my textbook, the give an example for finding maximal and minimal elements on a set. The set is $(\{2,4,5,10,12,20,25\},|)$. To find the maximal and minimal elements of the set, the draw a Hasse ...
1
vote
1answer
68 views
Partial Ordering and Covering Relations
I am currently reading about partial ordering and covering relations. I just want to be certain that I am understanding these concepts correctly. A partial ordered set (poset) is just a relation on a ...
1
vote
3answers
112 views
Describing A Congruence Class
The question is, "Give a description of each of the congruence classes modulo 6."
Well, I began saying that we have a relation, $R$, on the set $Z$, or, $R \subset Z \times Z$, where $x,y \in Z$. The ...
