Boolean Equation Problem

I'm struggling with the following problem.

I have a series of boolean equations. Only one of these equations can be true at any one time. I need to find an efficient way of determining which of these equations is true. I would also like to know more about these equations, like is it true that only one of the equations can be true and what new equations are needed to make that true.

Here's an example. Let's say that half of the equations deal with the condition where variable A issw equal to the value 'M'. 25% of the equations deal with the condition where variable A is 'm', 25% of the equations deal with the condition where variable A is 'n', 15% where the variable A is '?' and 10% where the variable A is 'N'. The variable B has a situation where 75% of the equations deal with the condition where it is 'M' and the other 25% of the equations are divided among the other choices. There are also variables C, D, E, F, and G. Which of these variables do I evaluate first? What factors should I consider? Are there algorithms that will help me in determining this?