Gate2018 cs Q59

59Let 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?

Option : D
Explanation :
P : Set of rational number → countable
Q : Set of functions from {0, 1} to N → N

0 can be assigned in N ways
1 can be assigned in N ways
There are functions, cross product of countable set in countable.
R : Set of functions from N to {0, 1}

Each of thus boxes can be assigned to 0 or 1 so each such function is a binary number with infinite number of bits.

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