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 $\lim _{x \rightarrow x_0} f(x)=f\left(x_0 \cdot\right)$ 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 $\lim _{x \rightarrow x_0} f(x) \neq f\left(x_0.\right)$

• A

  Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
• B

  Statement 1 is false, Statement 2 is true.
• C

  Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
• Correct answer
  D

  Statement 1 is true, Statement 2 is false.

Hence, the correct answer is option: 'D'.