Let $m, n$ be positive integers. Let $X$ be a non-empty set.
a. If $m$ is the less than or equal to n, find an injective map $f: X^m \rightarrow X^n$
b. Find a bijective map $g: X^m \times X^n \rightarrow X^{m+n}$.
I'm just looking for information on what exactly the question is asking. I figured for A the question is asking for a map from an element $X_i$ in $X^m$ onto the matching $X_i$ in $X^n$, since the question is only asking for injectivity and doesn't require the map to span $X^n$. I'm sorry if my formatting is confusing.