p.7: 9,18,29,35
p.14: 7,14
p.16: 9,14,15
p.18: 3

p.28: 4,8,12,13
p.37: 2,6,8,10,14
p.41: 6,8
p.44: 4,6,8,10

p.48: 2,10
p.51: 10
p.53: 6,8,10
p.57: 2,4,6,10

p.60-61: 2,6,8,10
p.100: 6,8,12,14,18,20.

p.110: 6,7,12,20,25,29
p.118: 4,10,17,20,24

p.83: 2,4,10

Prove that in any group of 100 people there are at least 15 people born on the same day of the week.

Show that among any n+1 numbers one can find 2 numbers so that their difference is divisible by n.

Given 12 different 2-digit numbers, show that one can choose two of them so that their difference is a two-digit number with identical first and second digit. Show on an example that this conclusion does not hold if we choose 11 numbers.

Prove by contradiction: If infinitely many objects are put into finitely many boxes, then at least one of the boxes will have infinitely many objects.

Day's book: p.11: Problem 1.13 and Problem 1.14.

Hammack's book: pp.129-130: 4,12,18,26,35,36

p.153: 8,14,18,22,24,30

Prove or disprove:

\( \mathcal{P}(A) \cup \mathcal{P}(B) = \mathcal{P}(A \cup B) \)
\( \mathcal{P}(A) \cap \mathcal{P}(B)=\mathcal{P}(A \cap B) \),
\( \overline{\mathcal{P}(A)}=\mathcal{P}(\overline{A}) \)

p.145: 4,8,18,26

p. 169-170: 2,8,10,12,18
Day's book: Problem 2.24, Problem 2.26 (c),(d).
Use strong induction to prove: if \( a_1=8, a_2=24, a_{n+1}=4a_{n}-4a_{n-1} \), then \(a_n=(n+1)2^{n+1} \).

p.178: 10
pp.182-183: 2,6,13
p.187: 2,6,8

p.204: 6,10,14
p.210: 8
p.214: 4,7,8,10
p.216: 6

p.222: 2,8
Let \( |A|=|B| \) and \(|C|=|D| \). Prove that \( |A \times C|=|B \times D| \).
p.228: 4,15