1. The problem states that for all $a \in A$ and $b \in B$, the sum of $\text{con}_a(t)$ and $\text{con}_b(t)$ equals 1, i.e., $$\text{con}_a(t) + \text{con}_b(t) = 1$$ 2. This implies that $\text{con}_b(t)$ is the complement of $\text{con}_a(t)$ with respect to 1. We can express this as: $$\text{con}_b(t) = 1 - \text{con}_a(t)$$ 3. This relationship means that for any given $t$, the values of $\text{con}_a(t)$ and $\text{con}_b(t)$ are dependent and sum to 1. 4. If you know one of these functions at a particular $t$, you can find the other by subtracting from 1. This is a fundamental property often used in probability and complementary functions.