# Tagged Questions

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### 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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### 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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### 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 ...
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### 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. ...
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### 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 ...