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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 âˆˆ Z}.

(d) If A, B are countable sets, then A â‹ƒ B is countable.

(e) If A, B are uncountable sets, then A â‹‚ 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.

(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 âˆˆ Z}.

(d) If A, B are countable sets, then A â‹ƒ B is countable.

(e) If A, B are uncountable sets, then A â‹‚ 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.

The set.

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