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Let N be the set of natural numbers. Consider the following sets. P: Set of Rational numbers (positive and negative) Q: Set of functions from {0, 1} to N R: Set of functions from N to {0, 1} S: Set of finite subsets of N. Which of the sets above are countable?

Let N be the set of natural numbers. Consider the following sets. P: Set of Rational numbers (positive and negative) Q: Set of functions from {0, 1} to N R: Set of functions from N to {0, 1} S: Set of finite subsets of N. Which of the sets above are countable? Correct Answer <em>P</em>, <em>Q </em>and <em>S </em>only

Set of rational numbers are countable.

Set of functions from {0, 1} to N is also countable.

Set of functions from N to {0, 1} is equal to number of subsets of N which is uncountable using Cantor's diagonalization argument.

Set of finite subsets of N has bijection with N.

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