Q39

Let $f: A \rightarrow B$ be an onto (or surjective) function, where $A$ and $B$ are nonempty sets. Define an equivalence relation $\sim$ on the set $A$ as

$$a_{1} \sim a_{2} \text { if } f\left(a_{1}\right)=f\left(a_{2}\right),$$

where $a_{1}, a_{2} \in A$. Let $\mathcal{E}=\{[x]: x \in A\}$ be the set of all the equivalence classes under $\sim$. Define a new mapping $F: \mathcal{E} \rightarrow B$ as

$$F([x])=f(x), \quad \text { for all the equivalence classes }[x] \text { in } \mathcal{E} \text {. }$$

Which of the following statements is/are $\text{TRUE}?$