Exercises:
- If
, show that
- Prove by induction on n that
has
subsets.
- Show that
- Show that
for each
- Show that
- Show that
- Show that
- Show that
and use Stirling’s formula to prove that
- Give a solution using binomial coefficients and a direct combinatorial solution to the following question: How many pairs
of subsets of
are there such that
?
- Show that the number of even subsets of
equals the number of odd subsets of
. Give two proofs, one using binomial formula, and one using a direct bijection. Calculate the sum of the sizes of all even (odd) subsets of
.
More later,
Nalin Pithwa