JEE Main 2011 Mathematics question

Let R be the set of real numbers This question has Statement −1 and Statement −2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1 : is an integer is an equivalence relation on R. Statement-2 : for some rational number α is an equivalence relation on R.

• (1)Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1
• (2)Statement −1 is true, Statement- 2 is false.Correct
• (3)Statement −1 is false, Statement −2 is true.
• (4)Statement −1 is true, Statement −2 is true; Statement −2 is a correct explanation for Statement −1