If either A is B or E is F, either C is D or G is H. Either A is B or E is F. .'. Either C is D or G is H. In this shape the likeness of the dilemma to the partly conjunctive syllogism is more immediately recognisable. The major premiss in this shape is vaguer than in the former. For each antecedent has now a disjunctive choice of consequents, instead of being limited to one. This vagueness, however, does not affect the conclusion. For, so long as the conclusion is established, it does not matter from which members of the major its own members flow. § 786. It must be carefully noticed that we cannot treat the complex destructive dilemma in the same way. If either A is B or E is F, either C is D or G is H. Either C is not D or G is not H. Since the consequents are no longer connected individually with the antecedents, a disjunctive denial of them leaves it still possible for the antecedent as a whole to be true. For 'C is not D' makes it true that G is H, and 'G is not H' makes it true that C is D. In either case then one is true, which is all that was demanded by the consequent of the major. Hence the consequent has not really been denied. § 787. For the sake of simplicity we have limited the examples to the case of two antecedents or consequents. But we may have as many of either as we please, so as to have a Trilemma, a Tetralemma, and so on. TRILEMMA. If A is B, C is D; and if E is F, G is H; and if K is L, M is N. Either A is B or E is F or K is L. .'. Either C is D or G is H or K is L. § 788. Having seen what the true dilemma is, we shall now examine some forms of reasoning which resemble dilemmas without being so. § 789. This, for instance, is not a dilemma-- If A is B or if E is F, C is D. But A is B and E is F. .'. C is D. If he observes the sabbath or if he refuses to eat pork, he is a Jew. But he both observes the sabbath and refuses to eat pork. .'. He is a Jew. What we have here is a combination of two partly conjunctive syllogisms with the same conclusion, which would have been established by either of them singly. The proof is redundant. § 790. Neither is the following a dilemma-- If A is B, C is D and E is F. Neither C is D nor E is F. .'. A is not B. If this triangle is equilateral, its sides and its angles will be equal. But neither its sides nor its angles are equal. .'. It is not equilateral.