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: $A=\{(x,y)\in R\times R: y-x \text{ is an integer}\}$ is an equivalence relation on $R$. Statement-2: $B=\{(x,y)\in R\times R: x=\alpha y \text{ for some rational number }\alpha\}$ 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. (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.
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: $A=\{(x,y)\in R\times R: y-x \text{ is an integer}\}$ is an equivalence relation on $R$.\\
Statement-2: $B=\{(x,y)\in R\times R: x=\alpha y \text{ for some rational number }\alpha\}$ 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.\\
(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.