If each of a syllogism’s premises are accepted as valid, the conclusion may also be valid. Logical validity, however, also depends on the form and figure of the syllogism, which both depend on the propositions of the syllogism. In categorical syllogisms, four different types of propositions are used to make up the premises and the conclusion.“A” propositions propose a universal affirmative, such as “all are .” For example “All cats are felines.”
“E” propositions propose exactly the opposite: a universal negative. For instance, “no are .” More demonstratively, “No dogs are felines.”
“I” propositions include a particular affirmative qualification in reference to one of the terms in the premise. For instance, “Some cats are black.”
“O” propositions are the opposite, including a particular negative qualification. For instance, “Some cats are not black.”

, By identifying which of the four types of propositions are used, we can reduce a syllogism to three letters to help determine whether it’s a valid form for the figure of that particular syllogism. Different figures of syllogisms will be described in a following step. For now, simply understand that you can label each part of syllogism – including each premise and the conclusion – according to which type of proposition they make to identify the syllogism’s mood.For instance, consider a categorical syllogism with the mood of AAA: “All X are Y. All Y are Z. So, all X are Z.
A mood refers only to the types of propositions employed in a syllogism of standard order – major premise, minor premise, conclusion – and may be the same for two different forms based on the figure of the syllogisms in question.
 A syllogism’s figure is determined by whether the middle term serves as subject or predicate in the premises. Recall that a subject is what the sentence is about, and the predicate is a word that applies to the subject of the sentence.In a first figure syllogism, the middle term serves as subject in the major premise and predicate in the minor premise: "All birds are animals. All parrots are birds. All parrots are animals".
In a second figure syllogism, the middle term serves as predicate in the major premise and predicate in the minor premise. For instance: "No foxes are birds. All parrots are birds. No parrots are foxes."
In a third figure syllogism, the middle term serves as subject in the major premise and subject in the minor premise. For instance: "All birds are animals. All birds are mortals. Some mortals are animals."
In a fourth figure syllogism, the middle term serves as predicate in the major premise and subject in the minor premise. For instance: "No birds are cows. All cows are animals. Some animals are not birds."

, Although there are 256 mathematically possible forms of syllogisms – since there are 4 possible variations (A/E/I/O) for each part of a syllogism, and 4 different figures of syllogisms – only 19 forms are logically valid.For first figure syllogisms, the valid forms are AAA, EAE, AII, and EIO.
For second figure syllogisms, the valid forms are EAE, AEE, EIO, and AOO.
For third figure syllogisms, the valid forms are AAI, IAI, AII, EAO, OAO, and EIO.
For fourth figure syllogisms, the valid forms are AAI, AEE, IAI, EAO, and EIO.
Recognize types of propositions.
Identify the mood of a syllogism based on its propositions.
Determine the “figure” of the syllogism.
Recognize the valid forms of syllogisms.
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