__RULES OF HYPOTHETICAL SYLLOGISM__

- From the truth of the antecedent we can infer the truth of the consequence and not vice versa
- From the falsity of the consequence, we can infer the falsity of the antecedent and not vice versa

__DISJUNCTIVE SYLLOGISM__

A disjunctive syllogism is an argument with disjunctive major premise and categorical minor premise that either affirms or denies the one alternative if the major premise and the conclusion is also categorical and equally affirms or denies the other alternative

There are two types namely the; modus ponendo tollens and the modus tollendo ponens

this is a disjunctive syllogism whose minor premise affirms one of the alternatives of the major premise, while the conclusion denies the other alternative.µ__Modus ponendo tollens :__

Either a is b or c is d or either a is b or c is d

A is b c is d

Therefore c is not d therefore a is not b

NB: the modus ponendo tollens becomes invalid when both the minor premise and the conclusion affirms

NB: the modus ponendo tollens becomes invalid when both the minor premise and the conclusion affirms

this is a disjunctive syllogism whose minor premise denies one of the alternatives of the major premise while the conclusion affirms the other alternative.__Modus tollendo ponens:__

Either a is b or c is d or either a is b or c is d

A is not b c is not d

Therefore c is not d therefore a is b

**DILEMMA**

A dilemma is a syllogism with a conditional major premise having more than one antecedent, and a disjunctive minor premise.

A dilemma can be considered constructive, destructive, simple or complex.

**Simple constructive dilemma**

This is one with two different antecedents but the same consequent for the major premise; the minor premise affirms the antecedents and the conclusion affirms the consequents.

IF a is b and c is d, then e is f or if a is b, then c is d and if e is f, c is d

But either a is b or c is d but either a is b or e is f

Therefore, e is f therefore c is d

**The simple destructive dilemma:**

it is a dilemma with two antecedents and two consequents in the major premise; the minor premise denies the consequents of the major premise and the consequents denies the antecedent.

If a is b, then c is d and e is f

But either c is not d or e is not f

Therefore a is not b

**The complex constructive dilemma:**

**It is **a dilemma with two antecedents and two consequents in the major premise which differ; the minor premise affirms the antecedents disjunctively and the conclusion affirms the consequents disjunctively

If a is b, e is f and if c is d, g is h.

But either a is b or c is d.

Therefore, either e is f or g is h.

**The complex destructive dilemma: **it is a form of dilemma in which the hypothetical major premise has two antecedents and two different consequents. The disjunctive minor premise denies the two consequents while the disjunctive conclusion denies the two antecedents.

FORMULA

If A is B then E is F and if C is D, then G is H

Either E is not F OR G is not H.

Therefore either A is not B or C is not D.