Let denote the lattice of all strong degrees (or Medvedev degrees) of nonempty (or effectively closed) subsets of the Cantor space , and let denote the lattice of all weak degrees (or Muchnik degrees) of nonempty subsets of . We show that is not a Brouwer algebra and is not a Heyting algebra. These give solutions to problems presented by Simpson in 2008 and by Terwijn in 2006.