1. Stated problem: We have the equation $A + B + C = 1$. 2. This is a linear equation relating three variables $A$, $B$, and $C$. 3. Without additional information or constraints, the solution set consists of all triples $(A,B,C)$ such that their sum equals 1. 4. For example, if you fix values for any two variables, the third is determined by rearranging the equation: $$C = 1 - A - B$$ 5. This represents a plane in 3D space. The equation is already in simplest form. Final answer: The set of all $(A,B,C)$ such that $A + B + C = 1$ or equivalently $C = 1 - A - B$.