Importance of the properties of relations

Question

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!

Answer 1

Since you are a CS major, you probably already know relational databases, which have huge applications.

Answer 2

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 ).