# Tagged Questions

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### Binary relation, reflexive, symmetric and transitive

I have a question regarding an image. I'm currently studying binary relations and the following image confused me: What got me confused is that the page from which I got the link ...
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### Describing relations

(a). Describe all relations $R$ on $A$ which are simultaneously symmetric and antisymmetric. (b). Describe all relations $R$ on $A$ which are reflexive, symmetric, and antisymmetric. I have no ...
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### Why are both of these not equivalence relations?

Can anyone tell me why the first set is an equivalence relation, and not the second? As far as I can see, both are reflexive, symmetric and transitive, but my books says only the second one is an ...
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### Question on increasing/decreasing subsequences?

Here's the question: Describe a sequence consisting from 1 to 10,000 in some order so that there is no increasing or decreasing subsequence of size 101. I'm not quite sure how to do this. My first ...
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### Is this poset a lattice?

Given the set $\Bbb Z^+\times\Bbb Z^+$ and the relation \begin{align*} (x_1,x_2)\,R\,(y_1,y_2)\iff &(x_1+x_2 < y_1 + y_2)\\ &\text{ OR }(x_1 + x_2 = y_1 + y_2\text{ AND }x_1 \le y_1)\;: ...
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### Symmetric relations

Let $A=\{ 1, 2, 3, 4 \}$ is $B = \{ (1, 2), (2, 1), (1, 3), (3, 1) \}$ Is $B$ a symmetric relation on $A$? I said no because not all $x, y \in A$ are in $B$ Is this correct?
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### Prove the relation to be a Linear Order.

Let (a, b),(x, y) ∈ R × R and deﬁne ≺ as follows: (a, b) ≺ (c, d) iﬀ a < c or a = c and b < d: Deﬁne (a, b) ≼ (c, d) if and only if (a, b) = (c, d) or (a, b) ≺ (c, d). Show that ≼ is a ...
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### How to solve recurrence relation: f(n) = f(n-1) + 2(n-1) when f(1) = 1?

I am just learning about recurrence relations, and this is an absolute beginner's question. I understand what's going on in the formula, but I have no clue how to write it's solution? This probably ...
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### $\beta$ as the relation “is a brother of”

So I have a question about relations. In particular, here is the formal question: Let $\beta$ be the relation "is a brother of" and let $\sigma$ be the relation "is a sister of". Describe ...
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### Abstract Algebra topic: Equivalence relations [duplicate]

If R1 is reflective and not transitive, R2 is transitive but not symmetric and R3 is symmetric but not reflexive. We need to find an example of a set S and the three relations R1 R2 R3.
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### relations - examples and counterexamples

The question is to find an example of a set $S$ and three relations $R_1$, $R_2$, and $R_3$ on it, such that $R_1$ is reflexive but not transitive, $R_2$ is transitive but not symmetric and $R_3$ is ...
let say I have $A=\{1,\dots,8\}$ I want to know the following things: what the number of relations on $A$? what the number of reflexivity relations on $A$? what the number of equivalence relations ...
### Partially ordered set Question : $A=\{1,2,3,4,5,6\}$ ,$R =\mathcal P(A) \times \mathcal P(A)$
I`m trying to prove that this relation is partially ordered set: $A=\{1,2,3,4,5,6\}$ $R =\mathcal P(A) \times \mathcal P(A)$ \$(B,C)R(D,E) \Longleftrightarrow (B \subset D) \vee ((B=D)\wedge(C ...