(10 points) Determine whether each of these sets is finite, countably infinite, or uncountable.
For those that are countably infinite, exhibit a one-to-one correspondence between the set of
positive integers and that set.
a) The integers greater than 10
b) The odd negative integers
c) The integers with absolute value less than 1,000,000
d) The real numbers between 0 and 2
e) The set $A \times \mathbb{Z}^+$ where $A = \{2, 3\}$
f) The integers that are multiples of 10
(5 points) Give an example of two uncountable sets A and B such that A – B is
a) finite.
b) countably infinite.
c) uncountable.
(6 points) Show that a subset of a countable set is also countable.
