Statement $1$: $A$ function $f: R \to R$ is continuous at $x_0$ if and only if $\lim_{x \to x_0} f(x)$ exists and $\lim_{x \to x_0} f(x) = f(x_0)$.
Statement $2$: $A$ function $f: R \to R$ is discontinuous at $x_0$ if and only if $\lim_{x \to x_0} f(x)$ exists and $\lim_{x \to x_0} f(x) \neq f(x_0)$.

• 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 $1$.
• D
  Statement $1$ is true,Statement $2$ is false.