Prppositions with two value cases are propositions that are considered in the context of two-valued logic and have an unary argument. These propositions have four truth functions. These truth functions are: “true-true”, “true-false”, “false-true” and “false-false”. Direct variations of biconditional and noninclusive disjunction propositions with two value cases have “true-true” and “false-false” truth functions. Therefore, positive and negative simple propositions and variations of the conjunction, disjunction, conditional, incompatibility, and joint denial, which have the “true-false” truth function and the “false-true” truth function, cannot be reduced to the direct variations of biconditional and noninclusive disjunction. In this study, by creating indirect biconditional and noninclusive disjunction that have a “true-false” truth function and a “false-true” truth function, it is revealed how propositions equivalent to positive and negative simple propositions and direct variations of conjunction, disjunction, conditional, incompatibility, and joint denial, which have the “true-false” truth function and the “false-true” truth function, can be created. In this way, it is revealed how the positive and negative simple propositions and conjunction, disjunction, conditional, incompatibility, and joint denial, which have the “true-false” truth function and the “false-true” truth function can be reduced to the variations of biconditional and noninclusive disjunction.

Indirect reduction, simple proposition, compound proposition, biconditional, noninclusive disjunction.