Theorem: Every subset of a countable set is countable. In particular, every infinite subset of a countably infinite set is countably infinite.
A) countably infinite as we have one-to-one correspondence between positive integers and negative integers.
B) countably infinite as it is subset of Natural numbers
C) countably infinite as one-to-one correspondence can be formed by $f(n)= 100-n$
D) uncountable as it is not possible to list all real numbers between $0$ and $\frac{1}{2}$
E) finite
F) countably infinite as it is subset of Natural numbers