Mathematics 220
Homework Set 9
Due: November 21
If you are using the 2nd edition, be careful — question numbers may not agree.
• 10.20, 10.24
• 10.26, 10.28,
• 10.42 (draw a picture and think carefully about cases)
• 10.46 (induction is your friend)
EQ1 Let S, T be sets. Prove the following
(a) If |S| ≤ |T | then |P (S) | ≤ |P (T ) |.
(b) If |S| = |T |, then |P (S) | = |P (T ) |.
EQ2 Consider the function f : (−a, a) → R defined by f (x) =
number and x ∈ (−a, a).
x
a2 −x2
where a > 0 is a fixed
(i) Show f is bijective.
(ii) What can you conclude about the cardinalities of (−a, a) and R?
(iii) What can you conclude about the cardinalities of (−a, a) and (−b, b) for a, b > 0?