Problem in gate1998-10 part b -

Question

Can someone help me in "part b" of this question- https://gateoverflow.in/1724/gate1998-10 .
I am still not able to understand why $R^0$ is considered here ? 
and what is $R^0 $?
Is it Equality relation?
Do we have to consider it in every question of this type ?

 

Answer 1

In relations $R^0$ is Always the Identity relation (Equality relation as you termed). We can prove it in 3 ways.

1. Just By-heart it and think of it as an Axiom of relations.

2. We know in Relation theory $R^n.R^0 = R^n$ where $.$ is Composition Operator (Composition/Composite of two relations)

We could even write $R.R^0 = R$, Now you need to think what should be $R^0$ in such a way that When any relation is Composed with it, results in the same relation. (Sounds like Identity element for Composition of relation)

3. Answer Why in General mathematics $n^0 = 1$ where $n \neq 0$. If you can answer that, You can answer why $R^0$ is always the Identity relation. 

Try it.

Comments

Okay. My bad. A misunderstanding. I apologize.

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Are aisa hote hai. I never mind :)

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I didn't understand this part " LCM of 3 and 5 is 15. So, m=0 and n=15"

can you please explain, how to get m and n