# 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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### Determine whether each of these combinations of R 1 and R 2 must be an equivalence relation.

I have this question but not really sure how to do it when there is union and interception symbol. I am easily confuse when this 2 symbol appear. From my understanding I know that equivalence relation ...
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### What is a geometric relation?

We will call a relation geometric if $∀x, y, z(xRy ∧ xRz → yRz)$ Prove that if a relation is geometric and reflexive, then it is also symmetric. I'm trying to solve this problem but I don't ...
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### Counting binary relations

Let $A$ and $B$ be finite sets, $|A| = m$ and $|B| = n$. How many binary relations are there from $A$ to $B$? As far I read from various resources, binary relations is nothing but just a typical (...
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### Number of reflexive relations on the set {1,2,…,n}

I am solving questions of a bachelors exam and was unable to solve this question and i am looking for help!! Find Number of reflexive relations on the set {1,2,...,n}. I know that R is called ...
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### Number of common elements in $A \times B$ and $B \times A$

This question was part of maths worksheet of my brother and I was unable to solve it. He studies in High Shcool. So, I am asking for help here. Let there are 5 common elements between A and B set. ...
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### What does “$A \leq B : \Longleftrightarrow A \subseteq B$ is an order relation of $\mathcal{P}(N)$” mean?

I have read the following in some exercise for discrete mathematics. Let $N$ be a set and $\mathcal{P}(N)$ be its power set. Then $A \leq B : \Longleftrightarrow A \subseteq B$ is an order relation of ...
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### How to find $R$ as a set of ordered pairs?

Suppose I am given a set $A = \{0,1,2,3,4,5,6,7,8,9\}$ and a relation $R$ on $A$ which is given by $x R y \iff y=2x+3.$ In order to write $R,$ how would I go answering this question? Would I just ...
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### Find general solution of linear congruence equation

Congruences are beyond my understanding, I do not understand at all, if you could explain it to me as simply as possible on this example, I would be very grateful: Find a general solution of linear ...
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### Algebra proof within relation problem

I need to show an equivalence relation on $ℕ$ defined as follows: $x$ ~ $y$ ⇔ $x \times y$ is a square Reflexivity: $x \times x$ is a square, so $x$ ~ $x$, so ~ is reflexive Symmetry: $x$ ~ $y$ ...
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### equivalence relations counterexample

I'm asked to either prove or disprove if the relation on all integers Z is an equivalence relation for x~y if and only if x+y is divisible by 3. From my understanding, the relation can't be reflexive ...
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### Determine $[1] =\{n \in\Bbb Z | 1 R n\}$

Let the relation $R$ be defined on the set $\Bbb Z$ of integers by $a R b$ if and only if $a^2 − b^2$ is an integer multiple of $3$. a) Determine whether $R$ is an equivalence relation. Either prove ...
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### If I have a certain relation R, how do I find R^2 and R^3? [closed]

Suppose I have A = {a,b,c,d} and R = {(a,b),(b,c),(c,b),(c,d)}. How do I find R^2 and R^3?
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### Relation that is reflexive but not transitive or similar.

During class we had to come up with relations that are reflexive, but are not transitive or similar. I know the definitions of these terms. If we have a relation defined by the triple $$r = (A, B, R)$$...
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### Relation with $sgn$

I have a problem with this task. If anyone had a similar problem it would help me. The task is: In the set $S\in[-\pi,\pi]$ a binary relation is defined ρ with $xρy⟺sgn(\sin(x-\pi))=sgn(\sin(y))$. ...
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### Relation p^3 on set

For the relation p = {(1, 4), (2, 1), (2, 3), (4, 2)} on the set {1, 2, 3, 4}, determine the relation p^3. I get that p^3 is p°p°...
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### Functions as arguments in relations

I have here a little problem, where I am just not really sure how to tackle this: Let R be a relation on the real numbers, with R = {(log2(x), x)| x e R+}. Determine whether this is a function and if ...
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### What does $\leq ^{-1}$ mean?

Just came across a question on my homework assignment. The only thing it says is: What is $\leq ^{-1}$? It is on chapter for relations. I'm guessing it means: $R \leq R^{-1}$, for $R$ being a ...
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