What conditions have be satisfied to be a subring?
Hello : I have a problem whit this exercise
Decide which of the following are subrings of the ring of all functions from the closed interval [0,1] to :
1)the set of all rational linear combinations of the functions sin (nx) and cos (x) where m, n
{0,1,2,...}
2)the set of all polynomial functions
3)the set of all functions that have an infinite number of zeros
2 is a subring but not 1 and 3, but I can not establish the conclusion good, I hope some help
Thanks