Prove whether the following sets are countable or uncountable.

To prove a set S countable, you need to provide a bijection from a countable set C to S

To prove a set S uncountable, you will need to either attmpt a diagonalization proof similar to Cantor's proof that the interval [0,1] is uncountable, or find a bijection from an uncountable set to S.

(a)

(b)

(c) (The set of all functions from N to just the numbers 1 and 2)

(d)

{zz E N} {zz E N}