Statement 1: A function $f: R \rightarrow R$ is continuous at $x_{0}$ if and only if $\lim_{x \rightarrow x_{0}} f(x)$ exists and $\lim_{x \rightarrow x_{0}} f(x) = f(x_{0})$. Statement 2: A function $f: R \rightarrow R$ is discontinuous at $x_{0}$ if and only if, $\lim_{x \rightarrow x_{0}} f(x)$ exists and $\lim_{x \rightarrow x_{0}} f(x) \neq f(x_{0})$. (1) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1. (2) Statement 1 is false, Statement 2 is true. (3) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1. (4) Statement 1 is true, Statement 2 is false.
Statement 1: A function $f: R \rightarrow R$ is continuous at $x_{0}$ if and only if $\lim_{x \rightarrow x_{0}} f(x)$ exists and $\lim_{x \rightarrow x_{0}} f(x) = f(x_{0})$.\\
Statement 2: A function $f: R \rightarrow R$ is discontinuous at $x_{0}$ if and only if, $\lim_{x \rightarrow x_{0}} f(x)$ exists and $\lim_{x \rightarrow x_{0}} f(x) \neq f(x_{0})$.\\
(1) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.\\
(2) Statement 1 is false, Statement 2 is true.\\
(3) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.\\
(4) Statement 1 is true, Statement 2 is false.