Corresponding conditional

In logic, the corresponding conditional of an argument (or derivation) is a material conditional whose antecedent is the conjunction of the argument's (or derivation's) premises and whose consequent is the argument's conclusion. An argument is valid if and only if its corresponding conditional is a logical truth. It follows that an argument is valid if and only if the negation of its corresponding conditional is a contradiction. Therefore, the construction of a corresponding conditional provides a useful technique for determining the validity of an argument.Either it is hot or it is coldIt is not hotTherefore it is coldEither P or Q Not P Therefore Qor (using standard symbols of propositional calculus):P ∨ {displaystyle lor } Q ¬ {displaystyle eg } P____________QIF ((P or Q) and not P) THEN Q or (using standard symbols):((P ∨ {displaystyle lor } Q) ∧ {displaystyle wedge } ¬ {displaystyle eg } P) → {displaystyle o } QSome mortals are not GreeksSome Greeks are not menNot every man is a logicianTherefore Some mortals are not logicians In logic, the corresponding conditional of an argument (or derivation) is a material conditional whose antecedent is the conjunction of the argument's (or derivation's) premises and whose consequent is the argument's conclusion. An argument is valid if and only if its corresponding conditional is a logical truth. It follows that an argument is valid if and only if the negation of its corresponding conditional is a contradiction. Therefore, the construction of a corresponding conditional provides a useful technique for determining the validity of an argument. Consider the argument A: