Abstract
Background: Propositions simplification is a classic topic in discrete mathematics that is applied in different areas of science such as program development and digital circuits design. Investigating alternative methods would assist in presenting different approaches that can be used to obtain better results. This paper proposes a new method to simplify any logical proposition with two propositional variables without using logical equivalences.
Methods: This method is based on constructing a truth table for the given proposition, and applying one of the following two concepts: the sum of Minterms or the product of Maxterms which has not been used previously in discrete mathematics, along with five new rules that are introduced for the first time in this work.
Results: The proposed approach was applied to some examples, where its correctness was verified by applying the logical equivalences method. Applying the two methods showed that the logical equivalences method cannot give the simplest form easily; especially if the proposition cannot be simplified, and it cannot assist in determining whether the obtained solution represents the simplest form of this proposition or not.
Conclusion: In comparison with the logical equivalences method, the results of all the tested propositions show that our method outperforms the currently used method as it provides the simplest form of logical propositions in fewer steps, and it overcomes the limitations of logical equivalences method.
Originality/Value: This paper fulfills an identified need to provide a new method to simplify any logical proposition with two propositional variables.
Keywords: Propositional logic, truth tables, propositions simplification, minterms, maxterms, logical equivalences.
Graphical Abstract
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