Valid Argument-Forms

•          Valid Argument-Forms

–        Modus ponens (method of affirming):

•          Premises: p à q and p, conclusion: q

–        Modus tollens (method of denying):

•          Premises: p à q and ~q, conclusion: ~p

–        Disjunctive addition:

•          Premises: p, conclusion: p | q

•          Premises: q, conclusion: p | q

–        Conjunctive simplification:

•          Premises: p & q, conclusion: p, q

–        Disjunctive Syllogism:

•          Premises: p | q and ~q, conclusion: p

•          Premises: p | q and ~p, conclusion: q

–        Hypothetical Syllogism

•          Premises: p à q and q à r, conclusion: p à r

–        Dilemma: proof by division into cases:

•          Premises: p | q and p à r and q à r, conclusion: r