The Relationship between Exclusive-Or and the Unique Existential Quantifier

Abstract

Problem Statement: The efficiency of computer architecture design is affected by the components used. Establishing a relationship between exclusive-or (XOR) and the unique existential quantifier provides alternative system implementations. Approach: Applications of XOR and the unique existential quantifier were explained. Then, prepositional logic was used to establish the relationship between them. Results: Different quantified assertions with two variables that use the unique existential quantifier were represented without quantifiers by using XOR. Conclusions: The unique existential quantifier and XOR were helpful in some computer architecture systems such as multiplexers, decoders and bus systems. The unique existential quantifier and XOR may be used interchangeably in some situations, but not always.