Countability of binary numbers (CSIR NET Dec 2016 Math.Sci. Part B)

This is a CSIR NET December 2016 Mathematical Sciences Part B Question. Question: Consider the sets of sequences X = {(x_n): x_n ∈ {0,1},n ∈ N} and Y = {(x_n) ∈ X: x_n = 1 for at most finitely many n}. Then 1. X is countable, Y is finite. 2. X is uncountable, Y is countable. 3. X is countable, Y is countable. 4. X is uncountable, Y is countable. Subscribe for more answers and solutions and answer key uploaded in coming days. Comment below if you want a specific question answered.

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