The weighing solution requires both Algebraic and Logical skills. In algebra a letter symbol abbreviates and represents something that is unknown. In the weighing situation it could be use of g to represent the genuine or good value, and x to stand for the unknown (and counterfeit) weight.

In Logic two notions are used. The first is set membership. We may see that x is not an element of a set of the w4 weighing elements. [This can be represented symbolically by {a, c, e}.] Also x could be seen to be an element of the intersection of {a, b} and {a, c, e}.

Finally, logic in the form of the implication symbol -> must be used to derive the solution.