Please do try the questions by yourself before resorting to these hints!
- {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.
- Yes, no, no, yes, no, no, yes.
- 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).
- m.n, m + n, 2m, 2m-1.
- 32.
- {{1}, {2}, {3}}, {{1,2}, {3}}, {{1,3}, {2}}, {{1}, {2,3}}, {{1,2,3}}.
- a ⊕ b.
- Just do it.
- {[(a ∨ ~k) ⇒ g] ∧ [g ⇒ w] ∧ ~w} ⇒ k which simplifies to true.
- Note the duality of A and IA.
- 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}.
- 1/e.
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