This problem is asking to prove that if there is a surjective (onto) function from set $A$ to set $B$, then the sets $A$ and $B$ are equinumerous (have the same cardinality).

To prove this:

1. If a surjection $f: A \to B$ exists, every element in $B$ must be mapped to by at least one element in $A$.
2. Since there is no element in $B$ that isn't mapped from $A$, this shows that the size of $A$ is at least as large as $B$.
3. If $f$ is surjective, a bijection (one-to-one correspondence) can be formed between subsets, implying that $|A| = |B|$.

Do you need a deeper explanation or examples? Here are five related questions to explore:

1. What is the difference between surjective, injective, and bijective functions?
2. How can a bijection be constructed from a surjection and an injection?
3. What are the cardinalities of common infinite sets, like $\mathbb{N}$ and $\mathbb{R}$?
4. Can a set have more elements than another and still map surjectively onto it?
5. How do you prove two infinite sets have the same cardinality?

Tip: For finite sets, a surjection automatically implies that the sets have the same number of elements.