Answer:

1. Categorical propositions are important in logic because they provide a way to make precise statements about the relationships between classes or categories of things. Through the use of the standard forms of categorical propositions (e.g. "All S are P" or "No S are P"), we can reason deductively and draw valid conclusions about the relationships between different categories.

2. The laws governing the logical oppositions include the law of contradiction, the law of contrary opposition, and the law of subcontrary opposition. The law of contradiction states that a proposition and its negation cannot both be true at the same time and in the same sense. The law of contrary opposition states that two propositions are contrary if they cannot both be true but they can both be false. The law of subcontrary opposition states that two propositions are subcontrary if they cannot both be false but they can both be true.

3.Logical opposition is the relationship between two propositions that have the same subject and predicate but differ in quantity (universal or particular) and/or quality (affirmative or negative). There are four types of logical opposition: contradictories, contraries, subcontraries, and subalterns. Contradictories are propositions that differ in quality and are negations of each other (e.g. "All S are P" and "No S are P"). Contraries are propositions that differ in quality and are both universal (e.g. "All S are P" and "No S are P"). Subcontraries are propositions that differ in quantity and are both particular (e.g. "Some S are P" and "Some S are not P"). Subalterns are propositions that differ in quantity and have the same quality but different scope (e.g. "All S are P" and "Some S are P").

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1. Categorical propositions play a crucial role in formal logic and reasoning. They are statements that assert or deny something about a class or category of objects. The importance of categorical propositions lies in their ability to express relationships between different classes or categories. By using specific terms such as "all," "some," or "no," we can make statements about the inclusion or exclusion of individuals within those categories. Categorical propositions provide a foundation for logical reasoning and help us analyze and evaluate arguments.

2. The laws governing logical opposition are fundamental principles that describe the relationships between different categorical propositions. There are four primary laws of logical opposition:

- The Law of Contradiction: It states that a proposition and its contradictory cannot both be true and cannot both be false. For example, if we have the proposition "All birds can fly," its contradictory proposition would be "No birds can fly." Both propositions cannot be simultaneously true.

- The Law of Contrary: It states that two universal propositions (where "all" or "no" is used) that refer to the same subject and predicate terms cannot both be true. For instance, the propositions "All birds are mammals" and "No birds are mammals" cannot both be true at the same time.

- The Law of Subcontrary: It states that two particular propositions (where "some" is used) that refer to the same subject and predicate terms cannot both be false. For example, the propositions "Some birds can swim" and "Some birds cannot swim" cannot both be false at the same time.

- The Law of Subalternation: It establishes a relationship between universal and particular propositions. It states that if a universal proposition is true, then its corresponding particular proposition must also be true. However, if the universal proposition is false, the particular proposition can be either true or false.

3. Logical opposition refers to the relationships between different categorical propositions based on their logical quality (affirmative or negative) and quantity (universal or particular). The concept of logical opposition allows us to evaluate the compatibility or incompatibility between propositions and draw conclusions about their truth values. It helps us determine whether propositions contradict each other, exclude each other, or provide partial information about the subject and predicate terms.