For $m, n \in \mathbb{Z}$, let $f_{m, n}: \mathbb{Z} \rightarrow \mathbb{Z}$ be the function defined as $f_{m, n}(x)=m x+n \quad$ for all $x \in \mathbb{Z}$.
Let $\mathcal{F}$ be the collection of all such functions, that is, $\mathcal{F}=\left\{f_{m, n}: m, n \in \mathbb{Z}\right\}$. Then

• A

  every element of $\mathcal{F}$ is bijective
• Correct answer
  B

  $\mathcal{F}$ has infinitely many elements which are bijective and infinitely many elements which are not bijective
• C

  $\mathcal{F}$ has only finitely many elements which are bijective
• D

  no element of $\mathcal{F}$ is bijective

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