Indicate whether the described function is a real function

a)the binary operation of addition of real numbers.

YES

b)the operation that corresponds each nonzero real numbers with its two square roots.

YES

c)the function that associates with each quadratic polynomial function p defined by y=p(x)=ax^2+bx+c with a not equal to zero the coordinates (r,s)of the vertex of the graph of p in the xy-plane

YES

d)the function that maps each positive integer into the number of its different prime factors.

NO

e) the function f with f(x)=0 for all real numbers x

NO

f)the Dirichlet function D with D(x)=1 if x is rational and D(x)=0 if x is irrational.

YES