Another day — let's solve it. Step 1: Identify the function's input and output. The function assigns to each pair of positive integers the first integer of the pair. Let the function be $f$. The input is a pair $(m, n)$ where $m$ and $n$ are positive integers. The output is the first integer of the pair, so $f(m, n) = m$. Step 2: Determine the domain. The domain is the set of all possible inputs. The problem states the input is "each pair of positive integers". A positive integer is an element of $\mathbb{Z}^+ = \{1, 2, 3, \dots\}$. A pair of positive integers is an element of the Cartesian product $\mathbb{Z}^+ \times \mathbb{Z}^+$. So, the domain is $\mathbb{Z}^+ \times \mathbb{Z}^+$. Step 3: Determine the range. The range is the set of all possible outputs. The output of the function is $m$, where $m$ is the first integer of the pair $(m, n)$. Since $m$ can be any positive integer, the set of all possible values for $m$ is $\mathbb{Z}^+$. So, the range is $\mathbb{Z}^+$. The domain is $\boxed{\mathbb{Z}^+ \times \mathbb{Z}^+}$ The range is $\boxed{\mathbb{Z}^+}$ Send me the next one 📸