Determine whether each of the following statements is true or false. For parts (d)-(g) provide a counterexample if the statement is false.
a) The set Q+ is countable.
b) The set R+ is countable.
c) There is a one-to-one correspondence between the sets N and 2Z = {2k|k ϵZ}.
d) If A, B are countable sets, then A ∪ B is countable.
e) If A, B are uncountable sets, then A ∩ B is uncountable.
f) If A, B are countable sets, then A – B is countable.
g) If A, B are uncountable sets, then A – B is uncountable.
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