1
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1answer
21 views

Composition of Ordered Pair

I'm doing math exercises from a Computer Science book and I am confused as to how the following result (from the solutions manual) is obtained: Given the function f={(a,b), (a,c), (c,d), (a,a), ...
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1answer
30 views

Need help with compositions of relations

Prove that given relations $R_1 \subseteq A \times B$, $R_2 \subseteq B \times C$, $R_3 \subseteq C \times D$ then $(R1 \circ R2) \circ R3 = R1 \circ (R2 \circ R3)$ I don't know where exactly to ...
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0answers
66 views

General (Set Builder) definition for a relation composed with itself n times

Questions What does the set builder notation for $S\circ R$ look like? I'm having the most trouble knowing when there is too much information or not enough information on either side of the 'such ...
2
votes
1answer
55 views

Does(n't) associativity of functional composition follow straightaway from associativity of relational composition?

One thing I find puzzling about the typical way in which associativity of functional composition is proved is that it makes explicit use of the fact that a function is a 'right-unique' relation, i.e. ...
1
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1answer
43 views

Suppose that $(X,Y,R)$ and $(Y,Z,S)$ are functions. Prove that $(X,Z,S \circ R)$ is a function [closed]

I am given this definition to help me with the proof: Suppose that X,Y and Z are sets, that R is a relation on X and Y and S is a relation on Y and Z. We define a new relation S ∘ R on X and Z as ...
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0answers
24 views

Restricting binary relations by composing with an “inclusion binary relation”

If $X' \subseteq X$ then we may define an inclusion map $\iota : X' \to X$ where $\iota(x) = x$. One use of $\iota$ is that we can express the restriction of some $f : X \to Y$ to $X'$ as $f|_{X'} = f ...
2
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1answer
236 views

Composition of two symmetric relations

Let $R1$, $R2$ be symmetric relations on a set. I want to prove that $R1\circ R2$ is symmetric if and only if $R1\circ R2=R2\circ R1$. I have tried a few problems of this type by doing something like ...
0
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1answer
77 views

Relation $R$: $R\circ R \subseteq R \implies R$ is transitive

Let $R$ be a relation on $X$, a set. If $R\circ R\subseteq R$, then is $R$ transitive?
3
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1answer
159 views

Diagrammatic (Postfix) Composition of Functions

Consider the functions $f : X \to Y$ and $g : Y \to Z$. According to the Wikipedia articles on Function Composition, the application of $f$ to an input $x$ can be written as $xf$ (as opposed to the ...
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1answer
711 views

What is the composition of relations like this? With no transitive relations between them?

Given $ R_1 = \{(1,2),(5,3)\}\quad\quad R_2 = \{(6,4),(5,7)\}$ What is $R_2 \circ R_1$? Because in my understanding, using the example $ R_3 = \{(1,2),(3,4)\} \quad\quad R_4 = \{ ...
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3answers
3k views

Composition of Relations

I'm in a bit confusion of understanding "Composition of Relations ". can someone help me up with an example. i have basic knowledge about relations, good explanation from some expert on this topic ...