1. **Stating the problem:** We want to understand when two finite sets $A$ and $B$ are called equivalent or equinumerous (equisovalent). 2. **Definition:** Two finite sets $A$ and $B$ are called equivalent (or equinumerous) if there exists a one-to-one correspondence (bijection) between the elements of $A$ and $B$. This means every element of $A$ pairs with exactly one unique element of $B$, and vice versa. 3. **Important rule:** For finite sets, this is equivalent to saying that $A$ and $B$ have the same number of elements, i.e., $|A| = |B|$. 4. **Explanation:** - If $|A| = n$ and $|B| = n$, then we can list elements of $A$ as $a_1, a_2, ..., a_n$ and elements of $B$ as $b_1, b_2, ..., b_n$. - Define a function $f: A \to B$ by $f(a_i) = b_i$ for each $i = 1, 2, ..., n$. - This function $f$ is a bijection, proving $A$ and $B$ are equivalent. 5. **Summary:** Two finite sets are equivalent if and only if they have the same number of elements. **Final answer:** Two finite sets $A$ and $B$ are equivalent (equisovalent) if $|A| = |B|$.