Answer "true" or "false" to the following statements:
1. If a standard-form categorical syllogism violates one of the first four rules, it may still be valid.
2. If a valid standard-form syllogism has an E statement as its conclusion, then both the major and minor terms must be distributed in the premises.
3. If a standard-form syllogism has two I statements as premises, then it is invalid.
4. If a standard-form syllogism has an E and an O statement as premises, then no conclusion follows validly.
5. If a standard-form syllogism has an I statement as its conclusion, then Rule 2 cannot be violated.
6. If a valid standard-form syllogism has an O statement as its conclusion, then its premises can be an A and an I statement.
7. If a valid standard-form syllogism has an E statement as a premise, then its conclusion can be an A statement.
8. If a standard-form syllogism breaks only Rule 5 and its three terms are "dogs," "cats," and "animals," then the syllogism is valid from the Boolean standpoint.
9. If a standard-form syllogism breaks only Rule 5 and its three terms are "dogs," "cats," and "animals," then the syllogism is valid from the Aristotelian standpoint.
10. If a standard-form syllogism breaks only Rule 5 and its three terms are "elves," "trolls," and "gnomes," then the syllogism is valid from the Aristotelian standpoint.