In this study, simple propositions and compound propositions are emphasized. Compound propositions, such as conjunction, disjunction, conditional, biconditional, incompatibility, joint denial and noninclusive disjunction are included. It examines which of these compound propositions can be directly reduced to their constituent simple propositions and which of them cannot be directly reduced to their constituent simple propositions. In this regard, the truth table method was used in the context of two-valued logic. With this method, simple propositions and compound propositions that are equivalent and not equivalent to each other are put forward, and it is tried to show which compound propositions can be reduced to their constituent simple propositions, and which compound propositions cannot be reduced to their constituent simple propositions. In this context, the following points are put forward: positive simple propositions can be reduced to the propositions of affirmed conjunctions with two positive components, the affirmed disjunctions with two positive components, the affirmed conditional with the negative leading component and positive posterior component, the affirmed incompatibility with both negative components, the affirmed joint denial with both negative components, the negated incompatibility with both positive components, the negated joint denial with both positive components, the negated conditional with the positive leading component and negative posterior component, the negated conjunction with both negative components, and the negated disjunction with both negative components. Negative simple propositions can be reduced to the propositions of the affirmed incompatibility with both positive components, the affirmed joint denial with both positive components, the affirmed conditional with positive leading component and negative posterior component, the affirmed conjunction with both negative components, the affirmed disjunction with both negative components, the negated conjunction with both positive components, the negated disjunction with both positive components, the negated conditional with negative leading component and positive posterior component, the negated incompatibility with both negative components, and the negated joint denial with both negative components.

Simple proposition, compound proposition, propositional connective, reduction, truth table