JEE Main 2023 Mathematics question

Let the sets A and B denote the domain and range respectively of the function f(x) = , where [x] denotes the smallest integer greater than or equal to x. Then among the statements (S1) : AB = (1, ) – N and (S2) : AB = (1, )

• (A)Only S2 is true
• (B)Only S1 is true
• (C)Neither S1 nor S2 is trueCorrect
• (D)Both S1 and S2 are true