(a) Prove that ll is uncountable. (b) Prove that there exists a denumerable subset S of ll. (0) Prove that for any nonempty sets A, B and C, if A is numerically equiv- alent to B and A n C = B H C = (D, then A U C is numerically equivalent to B U C. (Hint: Construct a bijective function g : A U C > B U 0. Verify that the function 9 you constructed is well-dened and bijective.) (d) Use the results from (b) and (c) to prove that l is numerically equivalent to R