Final answer:
When a universal affirmative statement ('A' statement) is true, other types of logical statements derived from it hold specific truth values. The 'I' statement is also true, the 'E' statement is false, option 'c' is not applicable, and the 'O' statement is always false.
Step-by-step explanation:
The student's question concerns the relationship between different types of logical statements, specifically focusing on the implications of a true universal affirmative statement, commonly represented by the symbol 'A' in traditional logic, derived from Aristotle's system of logic. When a universal affirmative statement ('All S are P') is true, it speaks to the categorical relationships between subjects and predicates. This question touches upon logical deductions and their relationships, as classified in the square of opposition, a diagram that Aristotle used to illustrate the logical relationships between certain types of categorical propositions.
Given that an 'A' statement ('All S are P') is true, then the truth of the other types of statements can be deduced as follows:
- The subcontrary 'I' statement ('Some S are P'), which is a particular affirmative, is also true because if all members of a set are part of another set, it is inherent that some members are as well. This means that option 'a' is incorrect.
- The subcontrary 'E' statement ('No S are P'), which is a universal negative, must be false because it directly contradicts the truth of the 'A' statement. This renders option 'b' incorrect.
- There is no sub-alternate 'L' statement in traditional categorical logic, making option 'c' nonsensical within this context.
- The 'O' statement ('Some S are not P'), which is a particular negative, is always false if the 'A' statement is true, for it contradicts the assertion that all members of the set are included. Hence, option 'd' is correct.
Therefore, if an 'A' statement is true, then the 'O' version of that statement is always false.