1. **State the problem:** We are given the function $F(x,y) = x + y + 1$ and want to understand or analyze it. 2. **Formula and explanation:** This is a simple linear function of two variables $x$ and $y$. The function adds the values of $x$ and $y$ and then adds 1. 3. **Intermediate work:** There is no simplification needed as the function is already in simplest form. 4. **Interpretation:** For any input values $x$ and $y$, the output is the sum of $x$ and $y$ plus 1. 5. **Example:** If $x=2$ and $y=3$, then $$F(2,3) = 2 + 3 + 1 = 6.$$