Please do try the questions by yourself before resorting to these hints!

1. {1, 2, 3, 5} and {3}.
   {1, 5} and {2}.
   {1, 5} and {1, 2, 3, 5}.
   {1, 2, 5}.
   {(1,2), (1,3), (3,2), (3,3), (5,2), (5,3)}, vice versa and Ø.
   {(0,1), (0,3), (0,5), (1,2), (1,3)}, vice versa and {(0,1), (0,3), (0,5)} ≈ A.
2. Yes, no, no, yes, no, no, yes.
3. Everybody loves somebody but there is not necessarily a single person who is loved by everyone else (or that person wouldn’t be single, presumably).
4. m.n, m + n, 2^m, 2^m-1.
5. 32.
6. {{1}, {2}, {3}}, {{1,2}, {3}}, {{1,3}, {2}}, {{1}, {2,3}}, {{1,2,3}}.
7. a ⊕ b.
8. Just do it.
9. {[(a ∨ ~k) ⇒ g] ∧ [g ⇒ w] ∧ ~w} ⇒ k which simplifies to true.
10. Note the duality of A and I_A.
11. Look back at Question 9 in the first set of exercises on induction. The subsets of {1,2,3} are Ø, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, and {1,2,3}.
12. 1/e.