Constructive dilemma
Constructive dilemma is a valid rule of inference of propositional logic. It is the inference that, if "P" implies "Q" and "R" implies "S" and either "P" or "R" is true, then either "Q or S" has to be true. In sum, if two conditionals are true and at least one of their antecedents is, then at least one of their consequents must be too. "Constructive dilemma" is the disjunctive version of modus ponens, whereas, destructive dilemma is the disjunctive version of "modus tollens". The constructive dilemma rule can be stated: where the rule is that whenever instances  of "formula_2", "formula_3", and "formula_4" appear on lines of a proof, "formula_5" can be placed on a subsequent line. Formal notation. The "constructive dilemma" rule may be written in sequent notation: where formula_7 is a metalogical symbol meaning that formula_5 is a syntactic consequence of formula_2, formula_3, and formula_4 in some logical system; and expressed as a truth-functional tautology or theorem of propositional logic: where formula_13, formula_14, formula_15 and formula_16 are propositions expressed in some formal system. Natural language example. The dilemma derives its name because of the transfer of disjunctive operator.