NPTEL Assignment Question

Question

Sir, kindly solve this. 

Answer 1

option A.  partial order

if you look closely it is the definition big oh notation which is partial order as we know.

why so ?

take example

f(x)=x^2

g(x)=x^3.

f(x)<= cg(x) for c=1 and n>1.

so f.g is in relation R.

now if it has to equivalence relation it has to be symmetric as well.

but here we cant say

g(x)<=c1f(x) for any value of c and n>n0.

so it is not symmetric.

 it is partial order because there are some function which we cant compare like for example sinx and cosx .

we cant say sin(x)<=ccos(x) it is not possible.

and it is antisymmetric as well so wecan say it is partial order not total .