There are a total of _______ syllogisms using all combinations of qualifiers for two premises and one conclusion.Only ____ of these syllogisms are valid.

Question

Quizplus · Accepted Answer

There are 4 types of propositions (A, E, I, O) and 3 elements (major term, minor term, middle term), leading to 4^3 = 64 combinations for each premise and the conclusion, totaling 64^3 = 262,144 combinations. However, considering the structure of syllogisms (major premise, minor premise, conclusion), the actual number of distinct syllogistic forms is 4^3 (for each of the two premises and the conclusion) times 3! (for the arrangements of the terms), resulting in 4^3 * 3! = 4^3 * 6 = 64 * 6 = 384. The correct answer, however, is not listed in the options provided, indicating a possible misunderstanding in the question or the options given. Among the provided options, 512 total syllogisms with 27 valid is the closest to traditional understandings of syllogistic logic, but it does not accurately reflect the calculation just described. The traditional count of valid syllogisms is indeed closer to 24 or 27, depending on the criteria used for validity.

There Are a Total of _______ Syllogisms Using All Combinations