If {n} denote the remainder when 3n is divided by 2 then

This is another way of solving the problem.

It is given that when 3n is divided by 2, the remainder is denoted by {n}. for all positive integers of n. This mean, {n} can be either 0 or 1 depending on whether n is even or odd. Now we need to find which of the following remainders result in 1.

This is like saying if f(n) is the remainder when 3n/2, then what values of the function results in 1.

1. {2n+1} is the remainder obtained when 3(2n+1) is divided by 2. ==> Obviously this results in 1.
2. {2n}+1 can be treated as the remainder obtained when 3(2n) is divided by 2 + adding 1 ==> Obviously this results in 1.
3. 2{n+1} can be obtained when 2 * 3(n+1) is divided by 2. This results in 0.

Hence my take will be C.