countable questions

1. E={x is belong to real #:tanx>=0}

2.
Let f1,f2,f3.....real #→[0,∞) be a collection of functions, for each n∈N, define

An(x) = {x belongs to real #,fn(x)=0}

We assume each An is countable.

a) Define a set

B={ x belongs to real#: f1(x)+f2(x)+....=0}

Is B a countable set?

b) Define another set

C= (x belongs to real #: (f1(x))(f2(x))....=0}

Is C a countable set?