WE HAVE TO USE the appropriate rules of inference in constructing formal proofs of arguments’ validity depending on the kind of propositions they use. The following are some basic techniques in properly constructing proof of validity of arguments.

1.Always begin by identifying the conclusion and attempting to look for it in the premises.

2. If the conclusion is a letter that appears in the consequent of a conditional statement in the premises, consider obtaining it through *modus ponens.*

3*.*If the conclusion is a negative statement (negated letter) that appears in the antecedent of a conditional statement in the premises, consider getting it using *modus tollens:*

4. If the conclusion is a conditional statement, consider obtaining it via hypothetical syllogism:

5.If the conclusion is a letter that appears in a disjunctive statement in the premises, consider getting hold of it via disjunctive syllogism.

6. If the conclusion contains a letter that appears in a conjunction in the premises, consider obtaining that letter via simplification...

7. If the conclusion is a conjunctive statement, consider obtaining the individual conjuncts first and then combining them via conjunction.

8. If the conclusion is a disjunctive statement, consider obtaining it either through addition or constructive dilemma.

9. If the conclusion contains a letter not found in the premises, addition mustbe used to introduce that letter.

10. Consider using conjunction to set up constructive dilemma and destructive dilemma. (Related: What is Moral Dilemma (And the Three Levels of Moral Dilemmas))

11. If the conclusion is a disjunctive statement consisting of two negated letters, consider using destructive dilemma.

12. If the conclusion is a conjunctive proposition and there’s a conditional statement in the premises which contains the letters in the conclusion, consider using absorption.

Remember too that the order of the premises does not affect the argument’s form. Keep in mind also that negative statements (negated letters) can be substituted in place of the P, Q, R and S of an inference form just as can affirmative statements.

Translate the following arguments into symbolic form and use the first four rules

of inference to derive the conclusion of each. The letters to be used for the simple statements are given in parentheses after each exercise. Use these letters in the order in which they are listed.

Notes on Natural Deduction @ www.OurHappySchool.com