For each of the following pairs, assume the first one is true and determine the truth value of thesecond.3. Some S are not PAll S are P is4. No S are P.All S are P is5. All S are P.Some S are P isTrue or False6. If a syllogism has an I statement as its conclusion, then Rule 2 cannot be violated7. If a syllogism has an E and an o statement as premises, then no conclusion follows validly
Advanced Placement (AP) · High School · Tue Nov 03 2020
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Let's analyze each statement:
3. Some S are not P
- All S are P is: False
4. No S are P
- All S are P is: False
5. All S are P
- Some S are P is: True (If all S are P, then at least some S are P)
6. If a syllogism has an I statement as its conclusion, then Rule 2 cannot be violated
- This statement is True. Rule 2 (Universal premises require a universal conclusion) is not violated when the conclusion is an I statement (Some S are P).
7. If a syllogism has an E and an O statement as premises, then no conclusion follows validly
- This statement is False. A valid conclusion can follow from premises containing an E statement (No S are P) and an O statement (Some S are P), specifically, the conclusion "Some S are not P.