1. The problem is to understand the difference between an onto function and a one-to-one function. 2. A function $f: A \to B$ is called **onto** (surjective) if for every element $b \in B$, there exists at least one element $a \in A$ such that $f(a) = b$. 3. A function is **one-to-one** (injective) if for every $a_1, a_2 \in A$, whenever $f(a_1) = f(a_2)$, it implies $a_1 = a_2$. 4. Being onto means the function covers the entire codomain, but it can map multiple elements of the domain to the same element in the codomain. 5. Being one-to-one means no two different elements in the domain map to the same element in the codomain. 6. Therefore, a function can be onto but not one-to-one if it hits every element in the codomain but some elements in the domain share the same image. 7. Example: Consider $f: \{1,2,3\} \to \{a,b\}$ defined by $f(1)=a$, $f(2)=b$, $f(3)=b$. This function is onto because both $a$ and $b$ are covered, but not one-to-one because $f(2) = f(3) = b$. This explains the concept clearly.