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 .
