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 $$a_1 \sim a_2 \text{ if } f(a_1) = f(a_2) ,$$ 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 $$F([x]) = f(x), \quad \text{for all the equivalence classes } [x] \text{ in } \mathcal{E}.$$ Which of the following statements is/are TRUE?

Let f : A B be an onto (or surjective) function, where A and B are nonempty sets. Define an equivalence relation on the set A as a1 a2 if f(a1) = f(a2) , where a1, a2 A. Let E = \[x] : x A\ be the set of all the equivalence classes under . Define a new mapping F : E B as F([x]) = f(x), for all the equivalence classes [x] in E. Which of the following statements is/are TRUE?

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