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Logic and Simplifying an Expression : Simplify min(a,b,c,d) + max(a,b,c,d)

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Simplify the following expression:
min(a,b,c,d) + max(a,b,c,d)
so that you are using three or less variables in each part of the equation.

Basically, they want the expression rewritten so that there is no "string" of four variables in it, and so it can be used to solve for the min and max. For example, assuming a and d are the min and max (the answer, however, should work for all variables), the expression should allow us to figure that out.

You CANNOT use nested expressions (like min(a, min (b,c))
You have to use 3 or fewer variables in all parts of the equation (for example, min(a,b,c) is OK, but min(a,b,c,d) is not)
You can have as many parts of the equation as necessary.

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Solution Summary

A logic expression is simplified and discussed in the solution.

Solution Preview

Let p = min (a, b, c)
Let q = min (a, c, d)
Let r = min (a, b, d)
Let x = ...

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