Composite function

Question

Given $A=\left \{1,2,3 \right \}$ and a relation $'R'$ on a set $'A'$

$ R = \left \{(1,2),(2,3),(3,1) \right \}$

$R^{2} = RoR;$ where $o$ is composition operation

Find $R^{25}=?$

$A) \left\{(1,3),(2,1),(3,3) \right \}$

$B)\left\{(1,1),(2,2),(3,3) \right \}$

$C)\left\{(1,2),(2,3),(3,1) \right \}$

$D)$ None of these

Comments

c?

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Yeah, but how?

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see we have R= {(1,2) ,(2,3),(3,1)}

                     R²={(1,3 ), (2,1),(3,2)}

                    R³= {(1,1),(2,2),(3,3)}

                    R⁴={(1,2),(2,3),(3,1)}.....

so we can observe that R repeats itself at an interval after degree 3...

∴ 25 % 3 = 1 ===> R²⁵ = R¹ = {(1,2) ,(2,3),(3,1)}

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@Shaik Masthan

How to find $R^{2},R^{3}$ and $R^{4}?$

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@shaikh brother can we use mod here? because we will have 0 values also means R⁰ if we take mod...(which is missing)

so i didnt took mod here...

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R2= R *R

R3=R2*R.....

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$R^{2} = RoR$

how to you right $*$ instead of $o$

I'm not able to understand

please explain more?

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its basically R o R i have tried to simplify that ...

see we have R2= (12 ,23, 31) o (12, 23 ,31)

                         = (12 ) o (12, 23 ,31)  v   (23) o(12, 23 ,31) v (31) o(12, 23 ,31)

                         =(now if (12) o(21) = (11) just remove common terms )

                         = and if (12 )o (23) = phi

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I don't understand what is the meaning of $RoR?$

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The composition of functions f : A → B and g : B → C is the function
gof : A → C given by gof (x) = g(f (x)) ∀ x ∈ A.

its same as writing RoR instead of GoF.

GoF, both are different functions

RoR, both are same functions

Answer 1

option C is correct . R⁵ is equal to R , R¹⁰ = R

so R²⁵  =R