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I get that relationships between things can be observed in our everyday life, but I fail to see how the properties of relations I have learnt in class can be applied to solving problems. Can someone give a few examples on how properties of relations are applied in real-life scenarios?

The properties being, reflexive, symmetric, antisymmetric and transitive.

I googled and looked into Rosen Discrete Mathematics And Its Applications but I couldn't find much. The most relevant post might have been this: Real life examples of order relations., where some examples were given, but I don't see how observing that certain things are reflexive etc can be helpful. Maybe I lack knowledge on some important theories that can be applied once these observations are made?

A CS major here, not a mathematician, a layman's explanation would be great :) Thanks!

IceTea
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  • For CS people: If a relation $\prec$ is not an order relation and you use it to build a binary tree by elementwise insertion (If new is $\prec$ the current node, insert on the left subtree, otherwise on the right), and if afterwards you then do a left-to-right tree traversal emitting nodes $x_1,\ldots, x_n$, it is not guaranteed that $x_1\prec x_2\prec \ldots \prec x_n$. -- Or if a relation is not an equivalence, you cannot succeed in finding a collection of representatives such that each object you encounter is in relation to one and only one of these representatives. – Hagen von Eitzen Nov 25 '19 at 07:43
  • Orders are used all over CS (stacks and heaps are a great example). Functions are relations, and they also are used everywhere. Equivalence relations are used in object-oriented programming. – Rushabh Mehta Nov 25 '19 at 07:51

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It can be useful to know that

  • the relation " a sexually desires b" is not symmetric ( one goes to jail for not knowing that)

  • the relation " a is friend with b " is not transitive ( therefore, it's not always a good idea to meet the friends of you friends)

  • the relation " a praises b " is not irreflexive ( some pathologic narcissists actually praise themselves)

  • the relation "a asks questions to b" is not symmetric ( knowing that will help not to have trouble with cops)

  • the relation " a gives orders to b " is , in a hierarchical context, antisymmetric ( you cannot give orders to your boss unless your boss is : yourself ).

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    This had me LOL-ing. I suppose knowing the properties expanded my vocabulary. Still, I could get away with just having common sense in all of the above :/ – IceTea Nov 25 '19 at 11:49
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Since you are a CS major, you probably already know relational databases, which have huge applications.

J.-E. Pin
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  • I do... but I don't see how knowing properties of relations would help in managing those databases? – IceTea Nov 25 '19 at 11:43