Let $S=\{(a, b): a, b \in \mathbb{Q}\}$ and $\ell$ be the line $y=m x+c$. Which of the following statements is not correct?

• A

  If $\ell$ passes through exactly one point of $S$, then $m$ must be irrational.
• B

  If $\ell$ passes through two points of $S$, then $m$ must be rational.
• C

  If $m$ is irrational and $c$ is rational, then $\ell$ passes through exactly one point of $S$.
• Correct answer
  D

  If $m$ is rational and $c$ is irrational, then $\ell$ passes through at least one point of $S$.

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